i usually just adapt to the enemy as far as my ships go, but here's a few designs that i never stop using:

the generator frigate. it basically just goes to a spot and cranks out power. it's designed to not be a major target of an attack, and sometimes, is the last thing standing after one.

the swarmer-fighter. cheap, agile, powerful. crank 20 of these at once and watch them overtake battleships.

automated scout drones. they're incredibly cheap. programmed to go after the control points. i can turn off the AI if i need them as cheap targets in case of an enemy cruise missile attack.

the cruise missile. rather fast, stealthy, and perfect at taking out densely packed fighter swarms.

the mobile defence platform. fairly cheap, and useful for fending off artillery and missile cruisers. not for missile-spam destroyers. those just shred everything.
here's also some of the ships i'm using right now:

the flak destroyer. as it stands, it's still imperfect, and not incredibly useful unless the enemy is really using a lot of fighters.

the missile-spam destroyer. it doesn't have a large range, but it's guaranteed that anything within range of it is already gone.