I'm going to say something blasphemous here. But I'll say it anyway.
It really doesn't matter. I have played 3 MP games, co-op. My buddy and I have wiped the floor with FEs and AEs let alone regular AI each and every time. It helps, yes, that we are together, but by the end, either one of us can take out an enemy empire all by ourselves, and rather quickly. In all 3 games I have used different load-outs. In the 1st game, I focused mostly on the supposedly gimpy missiles and fighters/bombers. In the 2nd game, I did mass drivers and plasma, but on separate ships, i.e., one ship would be all artillery, another would be all energy, so I had 2 designs for each ship class. Then I mixed and matched the fleet to about 50-50 of each type. In my current game, which is almost over (we just laid the smack-down on the final AE), I went mixed on each ship (i.e. each ship was half mass driver, half energy). I also varied ship composition. Game 1, my fleets were like 1 Battleship to 1.5 cruisers to 1.5 destroyers to 1.5 vettes. 2nd game it was 1:1:1:1. Current game it is 1 battleship to 2 cruisers to 4 destroyers to 8 vetts.
None of it mattered. I won roughly as easily regardless. There were minor 'flavor' differences to how things went, but overall my conclusion is, it really doesn't matter that much as long as your design isn't massively lopsided (e.g., all you have is nothing but cruisers with plasma and no other anything, yeah, that would likely cause trouble). The vette heavy fleets are easy to rebuild after a battle because vettes are quick and cheap to build. But... I have had massive frame rate hits when my 320 vette / 160 destroyer / 80 cruiser / 40 b'ship fleet went up against the AI with another large fleet. I tested this... I made another fleet that was just 40/40/40/40. I had both fleets in action against 2 different allied empires at the same time. When I zoomed into the one with the hundreds of vettes, my fps dropped to probably 2-3 per second. With the 40x4 fleet, it stayed reasonable (probably 18-24 fps though I did not track it). So I won't ever do the 'vette heavy fleet composition again, but only because of CPU performance, NOT because of battle performance.
So, I would say, do not worry about it too much. Keep your tech researched. Keep your ships upgraded. Build to your fleet capacity. And keep a fairly reasonable mix of ships per fleet (don't neglect any ship class dramatically). And you will be just fine against the AI.
Now, in MP that is a different story, but against the AI... really, I have found that just maxing everything out is all you need to do. Spread as much as you can in terms of territory. Colonize every world possible. Get as big as you can. Build a starport on every world. Upgrade the port to level 6 asap. Keep your pops happy and reproducing to max out that ship cap. Get the empire policy that lets you add to your ship cap. And then build to your fleet cap at all times, from the beginning of the game onward. This will keep you in the top of the power list, just below AEs, FEs, and maybe an advanced start AI or two, and soon you will surpass all but AEs. At this point, no one will attack you or threaten you, and you can win all battles against a single empire. Just watch for alliances. That's really where the AI can poke you if you aren't careful.
