A partial looks at warship roles...picking the best class and not just what is at hand.
BB, BC, CA & CL:
CV Escort: Not just the highest AA, but actually effective AA guns. Cannot be slower than the carriers. AS Radar a must. Fast BB are great here as they also draw dive bomber attacks protecting CVs even more (depends on how well your opposition uses DL).
Heavy SAG: For punishingh slugfests, lots of non rear firing guns. Ship repairs hopefully not too far away.
Light SAG: Low threat for plentiful skirmishing, lots of non rear firing guns torps great. Fast.
Raider: The ideal raider has plentiful endurance, a mix between good guns and AA, some ASW ability, radars, some air search is nice. A good example is the Brooklyn & Helena Class CL (no ASW but so much fuel to support a long legged destroyer) . For Japan think Maya.
If all else fails look here:
Fast Bombardment: If the ship doesn't go to the above uses, but has a speed of 8/9. Some invasions.
Slow bombardment: Pigs, need plentiful ASW & Air protection. Usually used only in controlled waters. Invasions.
CAP Trap Magnet: AA and maneuver.
Fast Minelaying: Has to have mines.
Fast Transport: IJN only.
SAG: Plentiful non rear facing guns, torpedoes, armor a plus
CV Escort: Good AA and ASW and Radar
ASW: Radar & plentiful ASW wpns
Fast Transport & APD: Clemson and Wickes & all IJN.
Screen: To provide proper screening of SAGs or finding minefields. Low VP. Use Aggressive captains...they won't last long but better them than a CA or fast BB.
There aren't that many great SAG DD: Fletcher, Porter, Mahan, Sumner, J Class, N Class, Aussie, French, perhaps Isaac Sewers? Those come to my mind very quickly for Allies.
In the early game, If you are planning on using American CVs, I would highly recommend sending over some British warships with air search radar via Australia. Also check your ASW escorts for night time experience!
Hard to over state the importance of adequate screens protecting larger ships versus torpedo strikes.