I spend a lot of time assisting fc, and I've seen every class successfully carry it with me or alone. For quickness, sure hands down, rogues, druids, and shamans. But they're all kind of squishy. The problem with shamans is that you can't cast and move (not too many instants), and throwing down totems pops you out of ghost wolf (and you can only talent wolf to instant if you are a 24 enhance). Rogues and druids are good because they can stealth in, but many many times I've seen them make it almost across field and die. Often times it seems both classes seem to think they can solo and outrun heals.
In my opinion, I'd say paladins and hunters are best fc's. I don't think that needs explaining as both are stupidly? great in this bracket. On the rare occassion I've seen mages in this bracket, they too make good carriers with blink and frost spells.
My favorite fc's though are the ones who have more than 1k health. Though I have seen a rogue with rez sickness, 200 health, cap it.