I just ran out of the RAF bonus. I leveled six full teams plus an all DK team. No matter what you choose questing will be like Khatovar described. I leveled two 5x same class groups and the rest were mixed. The mixed class groups were more fun to level.

If I was starting over without RAF and was making ONE group I would probably choose:

Paladin tank
Mage
Warlock
Cat druid
Priest

Paladin, because they're they easiest boxing tank. Mage because portals really help you travel when you can't chain summon yourself places using other toons' RAF summon. Lock because soulstone helps for wipes on bosses. Cat druid because they do great DPS. Priest because they're the best healer in the game.

This group has flexibility later. The paladin can tank, heal, or dps if you can get a ret rotation working. There's also the shockadin option. The druid can basically be a mage, rogue, warrior, or almost-priest. And the priest can be DPS, healer, or dps/healer.

Some people might switch out a shaman for the priest so you have a mail wearer for drops. I hate shaman though. Mages nuke better, rogues & druids melee better, and everyone else heals better. This has just been my experience. I've always preferred priests for healers and I always will.

You will need a healer and a tank class (according to blizzard) to use the dungeon finder.