Hmm, favorite ships...
This is a good one, but my absolute favorite has to be the Chronos-Class Battlecruiser from the Ship & Weapon Pack. It fits well into Starsector, and giving it the right loadout can overwhelm an enemy. Plus it's fast, has Time Accelerator (Capital Edition of the Temporal Shell) and a front-facing loadout (Missiles included). If put in the hands of an Aggressive captain, the Chronos can do a lot with it's loadout, whether it's a support loadout meant to shut down enemy ships engines, electronics, etc, or a Strike Loadout, complete with a Plasma Cannon and Phase Lances, with Typhoon Reaper Launchers.
In the hands of a player that knows what timing and when to go in to maximise potential, however...the possibilities are almost endless. Someone capable with a Doom, Falcon, or Scarab would love to use this ship. It's as if the Accelerator is too good for the Chronos itself somehow. I smash other fast ships with this, and the only few problems come from either boss ships, misplacement, carriers, or the occasional tough-hided ship, like the Onslaught. Nothing withstands the power of a Chronos for long. Time always tells of the result.
My second favorite has to be the Doom-Class Cruiser. That thing is vicious AND can avoid damage when it's neccessary. Escaping it is a nightmare if you're not fast enough, due to the Interdiction Array, which knocks out engines and the usability of the 2 main Medium Energy Slots crown this a winner over the Falcon, Nevermore, the Basilisk (Oculian Berserks Cruiser with two Freya revolving cannons, devastating as long as it can put down firepower) and even The END Carrier.
My third favorite is the Revenant-Class Destroyer. Weak armored it may be, but put it this way- armoring a Revenant as standard would make it overkill. This Revenant is able to use a special Temporal Shell that downright near stops time itself when you enter phase mode with it, making it apt for downright eliminating a Hyperion after it makes the very costly mistake of teleporting behind you. Tempests that don't have Heavy Armor and Reinforced Hull are also downright eliminated, and anything that gets shut down easily gets obliterated, especially engine wise. The Revenant is THE strike destroyer of choice, it's too bad it only gets a maximum of 300+ peak performance time and the Temporal Shell wears the Peak Performance time down when you phase with it. A close contender would be the Harbinger and the Medusa, due to their competition.
As for frigates, that's a tough one. Probably something like the Stymphal, Causality, or the Versant, for their versatility in combat. Stymphalian Birds make excellent harasser ships, the Causality as someone mentioned is a frigate eliminator, but is also a frightening opponent for anything below a cruiser, because of it's innate ability to send phase missiles out, while the Versant is an overall exceeder of a combat ship. The Excelsior is great too, just don't give it to a companion unless they know how to store energy.
EDIT - #1 - I cannot believe I forgot about the GMDA's renidition of the Falcon. Fast, powerful, capable. Not even frigates, except the Hyperion can escape this ship. I tested it myself after getting one in my Nexerelin playthrough. It catches practically everything, except the Hyperion and probably the modified GM-Stock ships, probably even the GMDA Wolf. But damn if it's fast. The only problem, which goes practically for every other GMDA ship, is the fact that it's PP time is significantly lowered due to extensive modifications to the stock body to make it the beast it is.
