My #1 go-to ship is infiltrators. I play very aggressively, preferring to launch long-range infrastructure raids, and these guys are perfect. Tractor beams won't slow them down because there's so many of them, and turrets and heavy defense have no chance against them. I can easily send my full cap of them (single player) deepstriking through 6 or 7 (diff 7) worlds if I do it right to pick off data centers or whatever else needs to be destroyed. They can also shoot through forcefields, ignore ship's defensive shields (bye bye space tanks), and damage engines (only 3-5 damage per shot, but 4 second reload and 1400 of them and they'll wreck everyone's engines). As such, unless I'm running an experiment, I will always choose infiltrators as my starting ship, they fit me so very well.
Past that,
I like:
Deflector Drones: Once I clear the wormhole, these guys (if I have them) are my next wave, because they can hold down a huge area of space with ridiculous damage potential (2,100 per shot at range 13,000 for mark 3? YES PLEASE).
Fighters: Cheap, lots of them, nice amounts of hitpoints, fast. Good against starships and bombers as well, which makes them an excellent complement to my infiltrator swarm.
Raiders: Fast, avoid defenses, I think their attack against turrets was nerfed though. If it was, they probably drop down to "ships that are okay".
Ships that are okay:
Spiders: Having the option to disable ships for easy mop-up is amazing, and the long range helps as well. Couple these guys with Deflector Drones or Snipers (or both!) and you've got a giant, almost-invincible long-range ball of doom.
MLRS: Better than a missile cruiser in every way except range. The problem is, I don't tend to build missile cruisers, so these guys aren't super useful for me either.
Laser Gatlings: Swarmy, decent damage. Don't really offer much that's special.
Snipers: Okay at range, good for laying down long-range suppression if you've got all of them in a giant mob. Also good for micromanage-free clean-up of raided planets.
Parasites: Expensive, high energy cost, weak attack, vulnerable, inefficient. If you set it up right these things can be amazing, but generally there are other ships I'd rather see from ASRs.
FF Bearer: Used to like them more, but the current unit cluster programming means they're terrible at protecting a blob. New clustering guidelines for this unit to try to avoid FF overlap and maximize FF coverage would maybe bump them up to "I like".
Raptors: Haven't spent a TON of time with these guys, but they've never really jumped out at me as "yeah, I'd like to see those from an ASR."
Microfighter: Stealth detect is nice. That's about all I really have to say.
Electric Shuttle: Decent on defense coupled with tractor beams, but weak attack and slow.
Ships I don't like:
Armor Ships: I feel like these guys are less effective infiltrators. Sure, the massive hitpoints are nice, but I generally don't worry about hitpoints and let numbers do the talking. I mean, anything that causes damage is not really a problem for infiltrators, it's the tractor beams they can't kill/disable. Having a lower ship cap than infiltrators simply means armor ships are even more vulnerable to tractor beams, especially if I want to do my long-range infrastructure raids.
Space Tanks: Too slow.
Cutlasses: Powerful, but can't target infrastructure and are way too slow to be effective on offense is what I find.
Vampires: Just seem weak all-around.
Zenith Bombards: Expensive, slow, fragile, relatively low damage. I'll use them if I've got them, but most of the time I've found they're a waste of resources, especially if I have some other ship type (like infiltrators) that wrecks defenses and infrastructure.
Bombers: Expensive, vulnerable, don't seem nearly as good against structures or defenses as they should be.
Missile cruisers: Slow, expensive, vulnerable. Only good for holding off fighters or in a pinch as ineffective artillery.
Acid Sprayer: Supposed to be a hard counter to zenith ships, I suppose, but they seem to be really bad at even that, and they're completely useless against anything else.
Unknown:
Teleport Battlestations
Eye Bots
Autocannon Minipods (didn't like them before the swarm bonus, haven't used them since the swarm bonus update)
Teleport Raider
Etherjet
Z Beam Frigate
Z Shredder
Z Mirror
Z Electric Bombers
Z Chameleons
Z Autobombs
Z Paralyzers
Sentinel Frigate
Bulletproof Fighter (Used them when they had lower hitpoints, they died like flies and were generally useless)
Grenade Launcher
Impulse Emitter
Shield Booster
Munitions Booster
Space Plane (Haven't used them much, but this is the one ship I hope to never see the AI with again, they are terrifying)
Anti-armor (Used them in the tutorial, they were okay then, as faster cheaper missile cruisers they hold some appeal)
I may have missed a ship or two, but those are my thoughts.
