Multigun corvettes are good against other corvettes and fighters. Heavy cruisers sound good, but they're way too slow to keep up with an attacking fleet. Pretty useless unless you get into a huge firefight or are playing defense. Carriers are a must for any fleet. They can take lots of damage and make great distractions for the enemy to attack.
Assault frigates are good against other assault frigates and corvettes.
Missle destroyers are great against smaller ships like corvettes and fighters. But don't count on them against other capital ships because their firepower decreases greatly after an initial burst of missles. Mine laying corvettes are good against capital ships if you have a small contingent of them, otherwise, they'll just get wasted. This is like a short tutorial. Just follow the computer's instructions and you'll be fine.