The idea is not to spam in this game. It's supposed to be designed towards combined arms strategies.
Considering the dedication to their game, IC designed it such that you should probably go with the balanced force.

There isn't supposed to be a paper rock scissors, though there are obvious counters such as the flak frigate against strikecraft.

And don't consider "zerg"ing in a game like this. It's a waste of time and other people's patience. This isn't your usual strategy game.

Otherwise, enjoy!

Carrier spam is easily countered by a handfull of flaks, and a regular fleet.

Fighters are quite useful, and if you are really worried about bomber fleets, just use only fighters on your caps... the fighter also gets a big damage bonus against... guess... LRMs

That is very important, as next to the Carrier the LRM is the next best ranged ship.

Notably, Bombers don't do so well against such ships either, they do well against Caps and Buildings, but only averagely against lighter fare; thus the LRM can do a great job at hammering carriers, as they are quick, long ranged, and the carrier is slow and also long ranged.

Bombers are a very effective tool in large quantities, but a good mixed fleet will beat them up; just be prepared to lose a capital ship. Also with fleet mechanics the Flak frigate does a good job now... they just don't stop the initial strike. You may not want to send a capital ship in against such a fleet... at least not right away; send in LRMs and Flak, the bombers will hit them up a bit, and then send in the capitals after the intial pay load is used.

Good luck.

Is there much difference between the fighters/bombers of each race? I think I saw that the big carriers have differing capacities, but what about the squadrons themselves?

I've found that fighters tend to distract enemy fleets while your big gunned caps and cruisers grind them down. Can be very useful support. I've not used a carrier based fleet though cause I don't like what happens when something big gets in close to them.

Carriers are also great raiders cause they can stay near the phase lanes and hit the enemy without taking any damage.

For a full fleet battle though they aren't so great. For support in that full fleet battle they're fantastic. Get your ships moving in a line and you can beat even a larger fleet by cutting off and eating small peaces at a time.