Vanilla:
Early game:
Early game is very volatile so hard to say. If it is the Apogee start, then well, the apogee, because it beats any of the easy to get ships by a large margin.
If it is not the apogee start, then I usually try and snatch a Pirate Mule or Pirate Enforcer. The obvious goal is to get a Monitor class frigate ASAP, because of the insane capabilities to tank damage. You can even stand in front of an onslaught for a while, and that's enough reasons to fly a Monitor!
Mid-Game:
Save up for an Eagle or an Aurora ASAP (depending on which one I am able to find)
Late-Game:
I usually stick with the Aurora because I don't really pilot ships if it's not absolutely necessary. If it gets uber-late game then Paragon.
Modded:
Early-Game:
I try to muster enough forces to visit The Hazard Mining Inc part of the sector, defeat as many DRACO fleets as possible and salvage whatever ships I possibly can. They're not amazingly great, but seems to be the easiest way to bolster the numbers. My flagship will be whatever I can salvage. There's a vanilla medusa that's also quite easy to salvage in the list of mods I like to play with, but don't want to give away the spoiler as to which mod and how.
Mid-Game:
Again, Aurora, it's just that good of a ship. Although I always leave it on auto-pilot.
Late-Game:
I stick with the Aurora, Sarissa (M) if I can find one (Mayasura Navy mod), or some bounty ship from one of the mods that provide special bounty ships as loot. (e.g. Vayra's mods)
Uber-Late game: Caliph Class from the Kadur Remnant mod.