Pre 2.00 I used to skip every ship class if possible to battleships. Almost never built more than a few corvettes, and those only to handle pirates and other early game threats. Was very rare I had to worry about an ai attacking me before I had cruisers or battleships. If I did, cruisers worked as a stop gap. Within 10 or so I had sufficient fleet power to kill any attacking corvette/destroyer swarm. By midgame all I would have is battleships. Nothing else was worth building in numbers.
Post 2.00 is very different. Corvettes are almost required spamming early game to prevent ai's from attacking you (at least on harder difficulties). There's some RNG there, if a neighbour ai is a wuss or has to deal with someone else or you make friends or varied other possibilities, then you can probably skip corvettes still to a degree. But they are generally much more necessary early and even late game. At end game now I tend to have 1-5 fleets of corvettes backing up my massive fleets of battleships. Lean towards more if I'm trading, less if trade is irrelevant.
However, battleships really blow everything away. Once you can build them in numbers, with decent techs, it is not practical to build anything else with the sole exception of anti-pirate corvette patrols and a cleanup fleet or two of corvettes to clear out outposts and stragglers while your fleet kills their fleet and bases.
I've found destroyers to be absolutely useless. Early game before evasion bonuses they are just weapon magnets. After that they are still weapon magnets, they just dodge sometimes. So far, every time I've tried them, in different roles, I'd have been better off just building more corvettes. I won't say they have no use at all, but that's how I feel right now. No matter how I spec them, no matter how many of them I have, no matter what other ships I have and what numbers they are at, destroyers always take all the shots and die every time. I could have one destroyer in a fleet of 200 corvettes, and the destroyer dies while every corvette walks away. Doesn't just happen with corvettes either. Throw a destroyer in with cruisers or battleships, the same result. Have a max fleet of each ship type go into a fight, the destroyers get wiped and everything else is peachy. At this point I don't build them any more for any reason. It's just a waste of alloys.
Cruisers are like mini battleships. They can take the place of battleships before you have them, but battleships are far superior so best to move past them asap. Still, they pack a punch and they have survivability well beyond destroyers and corvettes, and they are slightly faster than battleships are, so they can be quite useful under the right circumstances. Those circumstances don't last very long into the game, but they exist.