Lots of advice on offense, I'll give some advice for defense.
Use only survivable ships. Every ship should either have a respectable shield tank or phase capability. If you're going down the speed route, that means using (usually) small ships, and these die fast vs. Remnants. They're going to bring a lot of Sparks, which means countering fighters either with your own weapons or with your own fighters. I prefer fighters. Have all ships you field have a max level officer on board. If you're farming red Remnant fleets, you may even see cruisers start to die. My endgame farming fleet consisted of 3 Paragons.
These ships are able to survive yellow Remnant fleets:
Apogee: Best cruiser shield tank and only 18 DP. A little thin on the offense, but can mount Plasma Cannon.
Heron: Respectable shield tank, decent speed. There are better carrier options if you use mods.
Sunder: Great shield tank for its size. Make sure you fit shield mods and use them defensively.
Afflictor: Can distract, can sway difficult battles, but prepared to either babysit or lose these.
Have not tried but probably good:
Eagle, Aurora, Astral
Flagships:
Doom: Fantastic flagship that can wreak havoc and keep pressure off other ships even without shield tank.
Conquest: Works okay, but paper-thin if you ever run into flux trouble. Careful with this one.
Paragon: The be-all of Remnant combat. Shield system means you can hold out forever.
Have not tried but probably good:
Odyssey