The Conquest is my favorite ship so it always forms the core of my late-game fleets, though I have recently gained a liking to the Odyssey now that it got that speed buff. Helps that the Odyssey has a built-in hangar bay, which is what I focus my fleets on.
Fleet comp that I often return to:
1-2x Conquest / 1x Conquest 1x Odyssey, sometimes an Astral depending on what I plan on fighting
2-4x Heron
2x Medusa (Always named Terra and Luna, if anyone cares)
Assorted Wolf (Or Vigilance/Shepherd if I happened to salvage some)
Auxillary (Astral or 1-4x Tarsus, 1-2x Phaeton)
For the frigates, I don't personally care much for them so I don't focus on keeping them in the fleet if they happen to die: I'll take salvaged Wolf/Vig/Shep but I completely ignore Lasher and Hounds. If I happen to be fighting Tri-Tach and salvage higher-tech frigates I'll take those too, though.
My fleet revolves around heavy carrier presence and mobility. The Medusas act as surrogate frigates with far more firepower (any Wolfs are effectively just lower-strength Medusas and are equipped as such) while my flagship (Conquest or Odyssey) draws attention and tears apart anything that strays too close for too long.
For fighters, I equip the carriers with specific roles in mind- strike carriers are Longbow + 2x Khopesh while frigate-killers are 2x Broadsword + Warthog (sometimes Broadsword + Claw + Warthog, Claws can easily disable anything without a large shield so the Warthogs can eviscerate it), harassment or "space superiority" are either 3x Broadsword or a mix of Wasp/Broadsword/Claw. A heron with 3x Wasp is pretty hilarious to watch, though I can't say it really does all that much outside of completely shutting down any hopes the enemy had of a missile landing. My favorite fighter is the Khopesh, followed by Wasp and Claw wings.
If I hit that core fleet comp and keep playing for long enough I just get more Conquests and Herons. If it becomes too costly to fly around with them all, which it generally does given 4 capital ships are serious fuel hogs, I start dumping spares off at whatever market I've made my home- in the storage, that is. I'd never sell those beauties.