So after a lot of testing, I think I might have found the most OP fleet composition ever (without making specialized fleets for different fleet compositions).
What ships to use?
Research aside, I only use Corvettes and battleships. The basic strategy with this fleet is to have lots of Corvettes take all the fire while the battleships kill everything from afar. I don't use cruisers because they have an aggressive computer, so they charge in with the Corvettes and die, and that's a really expensive way to play. I don't use destroyers because, even though they have a defensive computer like battleships, they just don't have the firepower to compare with battleships, even when you factor in that one battleships equals for destroyers. Destroyers are fine to use before you research battleships though. When you use the ships, you'll find that you will very rarely have to replace battleships, maybe if you have to fight fleets from two directions.
How many Corvettes for each battleship?
I usually use a 1:3 ratio, so whenever I have a fleet with 20 battleships, I'll have 60 Corvettes (220 fleet capacity, usually around 20k power). You could use a 1:4 ratio, but I wouldn't go 1:2 because your battleships would start dying really early into the fight, and I wouldn't go 1:5 because that's just way more Corvettes than you need.
What weapons to use?
I always start it with kinetic weapons. Missiles are bad because they take too long to get to the targets, and are easily countered with point defense. I don't use lasers because they are good against shields, and not armor, and if you're playing against AIs, then they will always have both armor and shields. Kinetic weapons are fast, long ranged, and good against both armor and shields. With research, don't even bother with autocannons or Gauss cannons, you won't need them. You should just go straight for kinetic artillery, mega cannons, and giga cannons. You might realize that, while tachyon lances (which everyone loves for some reason) use X slots, like mega and giga cannons, kinetic batteries use L slots. In comparison, lasers and missiles have nothing like that at all, and kinetic artillery are just a little weaker than tachyon lances. So I'm your battleships, you should have a single giga cannon and all the rest kinetic artillery. On Corvettes though, since you can't have L slots and they're getting close to the enemy anyways, I use plasma throwers and disruptors. You could use some other close range weapon though, maybe autocannons?
Shields or armor?
For me, I always have to choose one, because it takes too much research to do both, but you can reverse engineer the one you don't use later. It's just a matter of opinion which one to use, but I would do armor, since lasers are weak against it. Missiles, on the other hand, take too long to get to your ships, and since kinetic artillery and giga cannons are so long range, they'll probably be dead by the time the missiles start hitting your ships (not late/middle game when you have fleets of 20k+ going around killing each other, and by that time you could reverse engineer level 5 shields easily).
Which ftl?
This really doesn't matter, just don't use hyperspace, since it just sucks (it was made to be limiting, but fast, but the warp cooldown time was buffed a lot so it's just limiting now). You can use warp or wormhole, it's just a matter of opinion. After a while, you can reverse engineer jump drive or psi jump drive once you kill your first fallen empire (also they have this awesome shield tech that gives you tons of shields in exchange for less hull points).
This strategy only has one real weakness, and that's if they somehow start shooting the battleships before the Corvettes. This can happen if someone warps on top of your fleet, you warp on a subspace snare that has a fleet waiting for you, or if someone attacks your side or from behind you. The strength of this fleet is a one on one long range battle. You have to remember to keep your distance, and attack them before they can even get to your Corvettes.
I have used this fleet type a lot, and I haven't seen any reason to use a different one, other than specialized fleets, which are very research heavy and require you to have lots of different fleets.
What ships to use?
Research aside, I only use Corvettes and battleships. The basic strategy with this fleet is to have lots of Corvettes take all the fire while the battleships kill everything from afar. I don't use cruisers because they have an aggressive computer, so they charge in with the Corvettes and die, and that's a really expensive way to play. I don't use destroyers because, even though they have a defensive computer like battleships, they just don't have the firepower to compare with battleships, even when you factor in that one battleships equals for destroyers. Destroyers are fine to use before you research battleships though. When you use the ships, you'll find that you will very rarely have to replace battleships, maybe if you have to fight fleets from two directions.
How many Corvettes for each battleship?
I usually use a 1:3 ratio, so whenever I have a fleet with 20 battleships, I'll have 60 Corvettes (220 fleet capacity, usually around 20k power). You could use a 1:4 ratio, but I wouldn't go 1:2 because your battleships would start dying really early into the fight, and I wouldn't go 1:5 because that's just way more Corvettes than you need.
What weapons to use?
I always start it with kinetic weapons. Missiles are bad because they take too long to get to the targets, and are easily countered with point defense. I don't use lasers because they are good against shields, and not armor, and if you're playing against AIs, then they will always have both armor and shields. Kinetic weapons are fast, long ranged, and good against both armor and shields. With research, don't even bother with autocannons or Gauss cannons, you won't need them. You should just go straight for kinetic artillery, mega cannons, and giga cannons. You might realize that, while tachyon lances (which everyone loves for some reason) use X slots, like mega and giga cannons, kinetic batteries use L slots. In comparison, lasers and missiles have nothing like that at all, and kinetic artillery are just a little weaker than tachyon lances. So I'm your battleships, you should have a single giga cannon and all the rest kinetic artillery. On Corvettes though, since you can't have L slots and they're getting close to the enemy anyways, I use plasma throwers and disruptors. You could use some other close range weapon though, maybe autocannons?
Shields or armor?
For me, I always have to choose one, because it takes too much research to do both, but you can reverse engineer the one you don't use later. It's just a matter of opinion which one to use, but I would do armor, since lasers are weak against it. Missiles, on the other hand, take too long to get to your ships, and since kinetic artillery and giga cannons are so long range, they'll probably be dead by the time the missiles start hitting your ships (not late/middle game when you have fleets of 20k+ going around killing each other, and by that time you could reverse engineer level 5 shields easily).
Which ftl?
This really doesn't matter, just don't use hyperspace, since it just sucks (it was made to be limiting, but fast, but the warp cooldown time was buffed a lot so it's just limiting now). You can use warp or wormhole, it's just a matter of opinion. After a while, you can reverse engineer jump drive or psi jump drive once you kill your first fallen empire (also they have this awesome shield tech that gives you tons of shields in exchange for less hull points).
This strategy only has one real weakness, and that's if they somehow start shooting the battleships before the Corvettes. This can happen if someone warps on top of your fleet, you warp on a subspace snare that has a fleet waiting for you, or if someone attacks your side or from behind you. The strength of this fleet is a one on one long range battle. You have to remember to keep your distance, and attack them before they can even get to your Corvettes.
I have used this fleet type a lot, and I haven't seen any reason to use a different one, other than specialized fleets, which are very research heavy and require you to have lots of different fleets.
) benefit mostly from going all in on the shields, as the math showed that no amount of armor stacking will benefit them much - they lack the hull hp pool to properly benefit of a percentage based damage reduction and they massively benefit from rapidly reloading shields. Try stacking their evasion - dodging hits goes great with the reloading shields, so prioritise the thrusters and combat computers over scanners. 
