If you can find a place where you can mindlessly grind.
Preferably via a one button mash...
Without much attention on the game, but enough to respond to a GM tell if you get one.
And have a tv/dvd player, in the same room.
That's an option (on a PvE server).
I've farmed (and watched the entire series of several shows, most recently a Battlestar Galactica marathon)...

I'd say questing will be the fastest method to level.
If you were to pick a single method to use.
Especially if you go with any of the quest stacking guides.
The Jaime guides are free for both factions; I personally use the Zygor Guides, with an in-game addon and arrow pointing where to go.
Collections suck, and Cataclysm quests are quite linear, although something like Zygor's is good for every other expansion...

But if you're doing several teams, one after the other, then you might be better off mixing it up.

You can bounce between teams, so you always have rested.
That should halve the entire process, give or take.

Any composition that is PvE worthy, will let you run dungeons.
If you have a Tank + Healer + 3x DPS, you can level via Dungeon Finder.

When your toons are 83-84, they'll do fairly well in PvP too.
Especially if you have a lot of the Cataclysm greens across the team.