I came up with five unique ones for three critical aspects of good sci-fi settings: FTL travel (technically there's a sixth I could have also used, but I chose not to), weaponry, and defenses.
The first method of traveling faster than light is through Wormholes. Wormholes are tunnels through space. Go in on one end, appear on the other, taking a 'shortcut' from one location to another. They are naturally occurring in sizes too small to readily utilize, but can be artificially created in two ways:
Worm Gates are man-made gates (think like a space-stargate from the later seasons of SG-1) that transport ships from one location to another. They are the default method of transportation, because they are safe, require next to no power, have no charge time, and travel is near-instantaneous. However, the downside of worm gates is that you can only go from one worm gate to another worm gate, and obviously to use one you need to be near one.
It is possible, but far more difficult, to use a Worm Drive to basically manipulate a naturally-occurring wormhole and artificially increase its size and alter its exit point. This has the upside of being able to use anywhere, but requires a feat of engineering, is reasonably large (you might find one on a medium-sized ship, but this is mostly something reserved for a bigger ship), and eats up a lot of power, with a little bit of charge time.
Still, it produces the same safe, instantaneous, almost-charge-free travel of a worm gate, so it is a viable drive to have installed on many ships.
On a lesser scale, a teleporter, something to transport cargo and humans alike, uses a localized version of a wormhole for short-distance transfers. These can be ship-to-ship or even deck-to-deck in a single ship. (Think the rings technology from Stargate SG-1.)
Slipstream is basically a "network through space". It can be thought of as a series of freeways and highways. Slipstream portals are preexisting; they cannot be man-made. They are a naturally-occurring series of interstellar roadways of sorts. In many ways, they combine aspects of wormholes, ftl drives, warp drives, and hyperspace: they basically accelerate objects within at an incredibly rapid rate, bending through a network of a space which connects space together but allows for shortened travel between point a and point b.
Slip Drives can be installed in a ship of any size, but again run into the problem that you need to enter pre-existing Slip Portals in order to use the slip drive. It has the upside of also requiring next-to-no power (similar to a worm gate), and also absolutely zero charge time (similar to a worm gate), but the downside of travel not being instantaneous and furthermore travel being dangerous. You can take a wrong turn, and you can have your ship be torn to shreds if it has what can be thought of as a car crash within slipstream.
Hyperspace can be thought of as "traveling through another dimension", or "traveling through a different plane", or "traveling through a space between/outside of space". It is basically a type of space entered, which isn't normal space, and traveling through this special 'hyper' space allows for travel at a speed greater than light. Any ship can have a Hyper Drive and you can use it anywhere, but hyperspace is not without its disadvantages.
It requires a slight charge to enter--not much of one, but enough to cause problems if you need to escape on the fly. It requires a little bit of power, so if you're running low, you're dead in the water. It is not instantaneous; of the FTL methods, it's one of the slowest to get you from point a to point b. And it is also hazardous; travel through hyperspace subjects the ship not only to the dangers of space but also the dangers of hyperspace, at the same time.
Still, because a ship of any size can use it at literally any point with fairly little energy expended, it is immensely useful for a bunch of ships who have need of FTL travel on a regular basis to locations that do not have preexisting exits.
A Warp Drive works by warping the space around the ship--the ship, technically speaking, remains stationary, but space around the ship bends, warping, such that the ship 'travels' from one location to another at a rate faster than light. Travel through Warp Space is one of the most common ways to travel. It can be used on a ship of any size, requires absolutely no charge time, can be used anywhere, and travel is safe using it.
It does have the downside that it is slower than most methods and it requires a fair amount of power (more than most FTL methods), but it is a fairly reliable, functional way of traveling on demand.
A FTL Drive works essentially by working as a bit of an inversion to a warp drive: instead of modifying space, the ftl drive modifies the ship. It has the effect of fundamentally altering what the ship is made out of (essentially), and then slingshotting this material to the target destination. Think of it as kind-of like long-range teleportation, sort-of converting mass to energy, shifting the energy to a different location at a speed transfer much faster than possible with mass, and then reconverting it back.
All within the blink of an eye, because it's faster than light. Ship's there, ship's gone; ship's not there, ship's suddenly there. This method of FTL travel has a lot of advantages; it's instantaneous (one of the only ones which is), inherently safe as a result, and can be installed in a ship of any size in any location. The disadvantage is this takes quite a fair amount of energy and it has a huge charge time. You can't, if suddenly under attack, instantly use it. Which means it is a bad idea to rely on it to get you out of trouble.
Related to this technology would be the transporter, which is...well, exactly what it is in Star Trek.
...You may notice some...rather questionable...usage of logic in justifying these five different methods of travel. I'm doing my best to take from their source materials and extrapolate from them how they'd work, when many of said source materials don't actually go into much if any detail about them.
Sure, the Stargate series explained how wormholes work quite extensively (and I believe in Farscape they work much the same way), but it also features hyperspace which they don't explain to my knowledge, and if you treat Destiny as a show which exists, technically also a FTL drive that they also don't really explain other than saying "it's not using hyperspace, it's using something more primitive" (which just so happens to function identically to hyperspace).
Trekkies could probably dissect the usage of Warp, but while I know some of how it would work, I'm far from an expert.
I'm pretty sure they never explained how FTL Drives work in Battlestar Galactica.
They explain a bit about Slipstream in Andromeda, but don't really go into much detail about how it functions, other than maybe that it might be something vaguely similar to wormholes except being different enough to not be wormholes.
Star Wars probably goes into hyperspace quite extensively in the legacy expanded universe canon, but even there my knowledge is fairly spotty.
I basically took some of the more popular works of science fiction that I am intimately familiar with (and did take some cues from other sources as well, e.g. Cowboy Bebop has gates of a sort as well), and tried to reason how a universe would work if all of them had basis in reality rather than just one, and thus, gave people options.
The one which didn't make the cut was the Space Dandy/Hitchhiker's Guide to the Galaxy (they're not quite identical but run on a similar enough premise) method of, "You travel from one universe where you were in one location, to a different universe where you are/just so happen to be in the target location. Technically, the old you dies in the transition, but you can't tell the difference". Which is a valid form of travel, just not one that I saw really having promising interactions with the others as much. (Also for symmetry purposes.)
As far as weapons go, I divided them into five types as well.
Projectile Weaponry is the "boring, but practical" default weaponry of the galaxy. This is a case of, quite literally, projectile weapons are just better. But there's actually justification for this! Projectile weaponry is just the most versatile overall weaponry of all.
For a start. It is one of only two types of weaponry which you can install en masse. A fighter can have half a dozen projectile weapons. A bomber, about a dozen. A medium sized craft, a few dozen; a large craft, literally hundreds. It can be used for point-defense, but it can also be used to bombard an enemy. Another advantage? Most projectile weaponry uses no power. Some does, but most can be used (albeit requiring manual operation) with absolutely no power at all, allowing for both defense and offense even when dead in the water.
Additionally, and this is the largest reason: projectile weaponry is, overall, the type of weaponry which can do the most damage to the most type of defenses assuming sufficiently energized projectiles. The equation relevant there is E = mc^2. Get a big enough mass of a projectile, and even if it's slow it can just plow through a defense (even if some of the mass is vaporized by the process); get a fast enough projectile, and so long as it doesn't lose all its mass (beit vaporization or from exploding on contact), it's guaranteed to puncture through.
Of course. Your average-day projectiles aren't gonna do that, so most projectile weaponry isn't that awesome, but it is still a pragmatic choice to implement. There's an obvious downside in that every type of projectile (aside from the hadron cannon) has ammo limitations (and if you run out of ammo, no more projectiles), but projectile weaponry is one of the fastest (well, with the exception of the hadron cannon) AND most deadly weaponry around, great for any purpose.
A sub-weapon within this type?
The hadron cannon. What is the hadron cannon? It generates a small black hole and launches it at high velocity. The hadron cannon is a special type of projectile weapon, however. It has two upsides: no ammo limit (you can fire as much as you want and never run out, so long as you have the requisite energy), and that if it hits the target, the target is destroyed. Understandably, a black hole has a LOT of mass. Launching it as a high-speed projectile adds a lot of velocity to it. No matter what your defenses are, there's no negating it.
This is not nearly as gamebreaking as it may sound, because it has many disadvantages.
For a start, it is a cannon. It is big. You might, MIGHT be able to fit one on a medium-sized ship, at the cost of great functionality to just about all other systems. You can probably fit two on a large craft, but three is nearly impossible.
It also takes a lot of energy.
You also have a tremendously long charge time. You can't just shoot it, then wait for it to recharch; you have to wait for it to charge and then discharge it eventually, minutes (yes, plural; it takes minutes to charge) later.
It is also borderline-suicidal for multiple reasons. First, if you start to charge the hadron cannon...you must discharge it. Failure to shoot it will result in it automatically discharging...at point blank, basically acting as a self-destruct for your ship because it will kill you if you don't shoot it.
Then, there's also the fact that as a cannon...it sucks at hitting rapidly moving targets. It might be able to hit a medium-sized ship if it's lucky, but anything smaller than that is a definitive no-go. Plus, given the long charge time...a common phrase surrounding it is more or less, "Hit your target, you win; miss your target or face more than one, you die".
Still, if you're in a situation where you need to take out a single large ship above all other targets, the hadron cannon is a fine weapon; if your target can't move, it's a fine weapon; in all other situations, it's "awesome, but impractical" personified.
A related, but separate, form of weaponry, what I dubbed:
Concussive Weaponry. What this basically is, in a nutshell? Explosions. Shockwaves. Force which rips apart the target, more or less. Where the damage comes from the blast. Nukes? Yep, they're concussive weaponry. They deliver an impact to the target.
Some concussive weaponry does in fact have limited ammo, but others can be unlimited, depending on the exact nature of the manufactured trauma force. Two forms of defense can basically nullify it, but the three other forms of defense can be torn to shreds by excessively powerful concussive force.
Like projectile weaponry, it can come in any size, from small to absolutely gigantic.
Heat Weaponry is basically exactly what it sounds. It is weapons which utilize heat to melt ships. Keeping in mind that weapons can be classified as multiple types, heat weaponry is often not purely heat. It most commonly overlaps with concussive weaponry (think the actual fireball part of a nuke in that it'd be ignited gasses) and energy weaponry. (Think beams, e.g. lasers, phasers, etc.) It is usually continuous, and thus, more likely to come in mid- to large-sized ships. (Though a small ship could have it if it were devoted to it.)
Energy Weaponry is next to projectile weaponry in how versatile it can be. It can be installed in any size, so like projectile weapons you can have half a dozen on a small ship, a dozen on a bombers, and so on and so forth. It can be rapid-fire, yet it can also be a continuous stream (think a beam weapon), or a ball, or basically...anything, really. It can use a little or a lot of energy, and the power behind it is proportional to the energy used. A little energy, a little damage; a lot of energy, a lot of damage inflicted. This makes it a secondary go-to weapon of choice.
Negating Weaponry is basically a disintegrator. Energy weaponry basically works by essentially overloading energy defenses and vaporizing the matter it makes contact with. (Namely, hopefully the other ship's hull.) Negating weaponry basically just makes energy and matter it contacts...no longer be there. There is almost no defense against this weaponry at all, and it can come in any size. It does have a disadvantage though; it requires more power to use than energy weaponry and it has a longer recharge time. Your first shot may be instantaneous, but there will be a gap between the first and the second shot, significantly longer than for energy weaponry.
Then comes what these weapons are put up against.
A ship could, theoretically, have all five types of weaponry, and even theoretically all five FTL methods. However, a ship cannot have all five defensive methods, as two are mutually exclusive with one another. Defenses are subdivided into two types--shields, and plating. The two hull platings are the mutually exclusive ones. The three shields can all be on the same ship...but only one shield type can be active at a time. If you use the reflectors, no deflectors or negators; deflectors, no reflectors or negators; negators, no reflectors or deflectors.
Organic Plating is exactly what it sounds like: living matter which not only can survive in space, but thrives in it, forming a type of exoskeleton around the outside of a ship's hull. (Notably, organic plating does not mean the entire ship is organic, simply that the outer layer of it has a 'skin' of sorts that is alive.)
Organic plating, being alive, is capable of regenerating itself over the course of a battle, allowing to heal from damage, softening the blows of early strikes having hit hard. This unique property is what makes it one of the only sources of protection against negating weaponry; it heals the wound almost as soon as it is inflicted.
Additionally, most organic plating has a property where it is capable of somehow absorbing shockwaves, negating the impact of concussive weaponry altogether. Organic plating also provides reasonable armor against projectile weaponry (both thanks to armor and due to gaps created healing), though this only protects against low-to-mid-level projectiles, and can still be severely damaged if enough projectiles get stuck in the organic plating (thus, interfering with the self-repair process).
However, organic plating provides absolutely zero defense against energy weaponry, and only the slightest mild protection against heat weaponry; the 'skin' is quite vulnerable to being superheated, charred, vaporized, and the like by a direct hit from those weapons, to the point where even small energy weapons can disable the plating.
Absorbent Plating/Conductive Plating has the effect exactly as you might expect: instead of energy passing through, when energy weaponry contacts this plating, it is absorbed, giving the ship energy. This means that a ship with this type of plating being blasted by energy weapons is actually gaining energy to use, with no limit.
This same property also provides minor protection against projectile weaponry. Small projectiles will have their kinetic energy absorbed as the projectile shatters on the plating, but it should be noted anything more advanced than a small projectile poses a threat. Medium concussive force also can be absorbed, but hit the plating with, say, a nuke and it'll still be torn to shreds.
The plating can also absorb a fair amount of heat weaponry, but an intense enough source of heat is still capable of melting through it. Also, this type of plating provides absolutely no resistance against negating weaponry, which can blast through the plates with ease.
Deflective Shielding does exactly what you would expect: it creates a shield around the ship, and deflects incoming weaponry to go elsewhere. This is one of the two main default forms of shielding, because it counters common forms of weaponry. Most projectiles, even ones with a huge mass, cannot puncture through the deflective shielding (after all, deflective shielding is used to divert large space rocks from hitting a ship), though a projectile with sufficient velocity and durability could accomplish the feat.
Heat weaponry is practically absorbed by deflective shielding, in that deflective shielding can basically suck the heat out. Energy weaponry is fairly effectively just harmlessly bounced off in a random direction. Concussive weaponry will have a warhead detonate upon contact. Even negating weaponry will when contacting the shield encounter difficulties.
It does have weaknesses, though. All deflective shielding operates on a frequency. Match the frequency, your weapons pass through. Concussive weaponry might have a warhead detonate on the deflective shielding, but the shockwave will still rip the ship to shreds because it'll pass right through the shield (so actually, hitting the shield makes concussive weaponry be arguably worse).
Negating weaponry can quickly cause the shield to disrupt and eventually fail, even if the shield generator is working perfectly. And even a sustained energy weapon will drain the deflective shield, in a match of atrophy: more power in the ship using the energy weapon, then the ship using the deflective shield runs out of power before the attack is halted.
Negating Shielding is the other common standard for shielding, acting as the counterpart to weaponry of its kind. (This is, for the record, Star Trek's type of shield, as I define it.) Projectiles touching the shield just cease to exist (unless they have sufficient mass to be protected). Energy contacting the shields is negated. Negating weaponry, meeting its counterpart, is itself negated.
However, negating shielding has its own weaknesses. It kinda sucks at negating heat build-ups. A single blast of heat will never do harm, not even if it is a super-intense form of heat, but a continuous blast of heat even if it is a weak blast will eventually melt through the shielding and pass on towards the ship.
Concussive weaponry works identically on it to deflective shielding, which means that hitting the shield actually helps the concussive weaponry destroy the ship. Negating shielding also works on a frequency, which if matched can be passed through. Furthermore, whereas deflective shielding can take a lot of long-term punishment and can be directed fairly effectively, negating shielding necessitates the usage of relays which if strained for too long are prone to failure.
Reflective Shielding can be thought of as basically a bubble surrounding the ship--and when something contacts the bubble, the bubble shrinks, shrinks, shrinks, and shrinks, slowing the thing down until it launches back out, forcing it at the original source.
This is really good for projectiles, though projectiles of a certain large size or speed can puncture through. (Especially speed.) It is also a way to altogether neutralize concussive force, as the concussive force simply bounces off the reflective shield harmlessly. Reflective shielding also has the upside of not operating on a frequency, which makes it impossible to bypass by matching the frequency.
...However, it has its downsides. Namely, reflective shielding can only reflect weak-leveled energy weaponry; anything bigger than that will destroy the shielding, as if popping a bubble, or tearing a hole in a beach ball, more aptly. Heat weaponry isn't nullified by it nor is it vulnerable to the heat, with them more or less canceling out if the heat isn't continuous. Any continuous heat however will absolutely melt right through. And negating weaponry tears through reflective shielding like wet tissue paper, as if it wasn't even there because as far as the negating weaponry is concerned, it might as well not be.
Other sci-fi stuff I threw around included at least two methods of FTL communication, from signal relays (basically like a future-cable-internet type deal of sorts, where the signal travels at a speed which is instantaneous so long as you are connected to one nearby), and from signal compressors (basically converting the communication in live time to an energy form sent in FTL travel).
And maybe for power, dark energy/dark matter if antimatter isn't enough.
Didn't really do much coherent beyond that though. Don't really even have a setting in mind. It's just...random stuff that I decided would be together, really, working with my absolutely atrocious understanding of the science behind sci-fi, blending various softer sci-fi stories into one.