My thoughts.
Triangle Ships
All fine. Fighters die quickly and their effects are hard to notice in a pitched battle, but when they're paired up against small things or things they have a bonus against, you see those things melt. Missile frigs don't seem to get a lot of love around here (idk why), but their range is very useful and they always seem to be the last thing standing. Plus their shots (and thus, what they kill) are very visible, which makes giving them credit easy.
Things like space tanks, bulletproof: more triangle ships. Nothing more needs to be said. Note that the zenith bombers aren't polycrystal, which is a blessing (fewer things tend to annihilate them) and a curse (can't touch fortresses).
The Maw
Amazing. Probably my favorite ship. Early-mid game they are completely unstoppable. Not even starships effectively remove one enemy ship from combat every one-two seconds, even from under force fields (eat your heart out, plasma siege). I haven't had the chance to play around with them late-game, when fleet sizes scale way up, so I expect them to be a little worse then. But not that much worse, since you still have... what, 20? of them, more if mk. v maw fabs exist. They do have the unfortunate effect of making battles suddenly turn catastrophic, as when one gets popped it dumps out a whole bunch of ships, but those ships weren't firing on you before, so it evens out.
Armor Rotter
That's a lot of armor damage. Big things die noticeably quicker when these guys are around, which I appreciate. They seem rather expensive though, esp. since you would probably be doing more raw damage if you had a different ship type. I don't mind getting these, they're neat.
Shield Bearer
My fleets tend to last a good 20-30% longer (very rough estimate) when these guys are around. They act as a force multiplier. Good stuff, although when you're actually in battle it's really depressing to see their shields deplete immediately. They also mean you have to keep your fleet together, making both x and v-moving a lot less useful.
Munitions Boosters
Incredibly good. Unsung facts: not only do they do really good damage to missile frigates, they have the range to hit them. My major problem with them is that, every time I see them, I always get tempted to invest 10k into the zenith/spire starships instead (I would love to hear how well the starships do at attack boosting your fleet late-game, for those who've had the opportunity to try).
Sniper
A+ on defense. The thing that makes me hesitant is that I have no idea how to use them on offense. Moving them into a system seems to aggro most everything, even though they don't seem to be actively targeting inactive ships? Also, invading a system defended with these reminds me of how broken blade spawners were a few months ago (I got the game just before that was patched, fun stuff).
Beam Frigate:
Underwhelming when trying to conquer planets. But vs waves or things like the fallen spire chase sections, they obliterate lines of ships at once, and at long enough range that often the AI doesn't get to fire.
Elec Shuttle:
They get better the harder the battle gets. DPS is great, but they don't have benefit of focus fire, which means that their dps doesn't actively deplete the AI dps, meaning you'll take more damage in the interim. Idk if I'd pick them as a starting ship, but they are very welcome from an ARS.
Ships I actively avoid using:
Gravity Ripper: why do both these and Gravity Drains exist?
Teleporters: Aside from hunting down things with retreat range, I have never found a use for any of these. I usually play with teleporters off.
Infiltrators: Their main use seems to be murdering power generators or command stations. The AI unfortunately has none of the former, and the latter you can substitute raid starships for. They don't do enough damage to really take out fleet ships under forcefields (a single laser or flak guardian would probably murder a whole cap by itself).
Space Plane: No damage. I thought I was really clever when I saw their bonus against ultra-heavy and thought "hey, I could help my bombers against fortresses with these, since their radar damping makes the fortress unable to hit them!" Unfortunately, the fort's armor ate the damage bonus wholesale, so the bonus to ultra-heavy is basically a sick joke. They maybe saved one or two waves of fire from the (only mk. 1) bombers. Better than the other spammable cannon fodder (go away, laser gatlings, you slow the game down too much to be worth your low dps) in that they survive more, but that's about it.
Younglings. Ugh. Wish there was some way to turn hybrids on without also turning these guys on (if I made a Mantis suggestion for disabling Younglings in ship type selection, would anyone vote that up?). Maybe I should try them again now that they've been buffed a bit.
Ships that sound interesting and I need to try sometime:
Spire Stealth Battleships and Blade Spawners: Their stats look incredibly good, but only 5 per cap? I can never bring myself to select them, because their numbers are so limited. Dunno how they actually play; they seem to be getting some love, so maybe I'll finally try them out soon.
Vampire Claw
Mini-rams
Tractor Platforms
Paralyzers