It's Battleship, Carrier, Colony, Siege, and Support.
The Radiance and Phase battleship are both excellent against other capital ships because of their anti-antimatter abilities.
The Kol is a little different. The most useful general combat ability it has is Flak Burst, which can ravage enemy fighter groups no matter how big they are. But it's not much better than any other capital against enemy capital ships, since Gauss Blast costs so much antimatter and doesn't have any non-linear effects.
Something not widely known, even though it's in the description, is that the Kol gets splash damage attacks on its autocannons while Finest Hour is activated - 60 bonus damage to every target in a small radius on every autocannon shot. To put that into perspective, a level 6 Kol will do 35 damage on the front/right autocannons and 64 on the left/back autocannons. (Those facings are not typos.) So not only do the autocannons more than double in damage ability, that damage bonus applies to every frigate near their target...!
Flux field works well with Gauss Blast though.
Flux operates for 60 seconds, and Gauss has a 6 second cooldown. Taking into account practical problems, a Kol can get off 7-8 gauss blasts during that 60 second period. With level 2 gauss blast, that's 3850-4400 damage; with level 3 gauss blast, that's 5600-6400. Mix that with Designate Target for great jusice.
Of course, to put that into perspective, a Missile Barrage does 3000 damage to every target and only takes 20 seconds. Lawl.