It kind of changes during a playthrough, depending on my goals and where I'm at. For the flagship, I start with SO Hammerhead. That takes me through much of the early-mid game. Then once I get some Cryoblasters it becomes the SO Medusa with dual Cryoblasters. For both of these, the battles are very much arcade-style, i.e. constantly maneuvering back and forth, poking at weak spots in the enemy fleet, etc.
Late game it becomes Onslaught XIV, with Proximity Charge Launchers. Basically run into the middle of the fleet and kill everything. At this point it becomes more strategic instead of arcade so I end up running battles at 2x speed (also, the Onslaught is slow, heh).
For the rest of the fleet, early on, I go for LP Brawler which takes me through faction fleets and into single Ordos. After that, there's a lot that I could go for, but typically I use mostly cruisers and capitals. I just envelop the enemy fleet at the beginning by spreading my fleet out into a line, and then they gradually fight toward the enemy spawn point, thus preventing ships from getting through.
As for which cruisers, Gryphons are easily the most overpowered (and thus easiest), but Apogees, Eradicators, Champions and surprisingly, the Eradicator (P) work pretty well under AI control. For sheer efficiency though, Conquests seem to be pretty good. For double Ordos, pretty much the fastest farming fleet I've found is flagship Onslaught XIV up the middle, with 2 Conquests on each side. That's only 200 DP against 240 DP (battle size 400) but it can handle it no problem and I don't have to worry about capturing points, since with BotB I can deploy all of that at the beginning. It's also a small enough fleet XP-wise that I can get +500% XP bonus out of it against double Ordos. Usually takes around 5 minutes per fight.
Attached is a screenshot of this setup, with Conquests 1 and 2 having their weapons on the right, and Conquests 3 and 4 having their weapons on the left. "Right sided" Conquests naturally drift to the left of the map as they fight, while "left sided" Conquests (and Odysseys) naturally drift to the right of the map as they fight, so I let them go to either side and I fight up the middle and clean up. You can see that the Conquests can fire their Squalls/Mjolnirs/HVDs/Harpoons from outside enemy range, so they don't take much damage, and the enemy ships that make it through are going to be no match for me. So I just need to press R on new target every so often and burn drive forward to make sure I have something to hit.