I have so many favorites, it is hard to choose one, so I will just list them by size.
Frigate:
Defiantly the Tempest. Put a heavy blaster on one side (I prefer the left) and a graviton beam on the other, augmented engines, extended + hardened shields, the rest in flux. Can outrun almost anything on the map and can hit hard enough to take down cruisers (even capitals if you are good).
Destroyer:
I am not particularly fond of destroyers, but my favorite would have to be the Medusa. Good speed, good shield coverage, a nice teleport, and enough firepower to really hit home. Although it is a very capable ship, I feel it is somewhat outclassed by ships like the Apogee and the Aurora.
Cruiser:
I used to swear by the Aurora, but since it's amazing shield ratio got nerfed, it has been replaced by the Apogee as my favorite. With enough skill points placed in the proper places, the Apogee can support an autopulse laser, two heavy blasters, and PD firing non-stop with extra flux for two anti-matter blasters to fire every now and again. It's speed pared with it's extra range form the sensor drones and great shield ratio makes the Apogee my mid-late game flagship.
Capital:
I tend to stay away form cap ships due to their lumbering nature, but recently i have been experimenting with the Odyssey and have found it to be a well rounded ship. It has enough speed to chase down cruisers and destroyers, enough flux to fire the big guns, decent shield coverage, excellent PD, and even a flight deck to boot. With enough tweaking it can easily take down an Onslaught and can go toe to toe with a Paragon.