I find it a pain in the butt to keep up with one class and one race. I can only imagine how hard it would be to do with this setup. I don't know about the Priest or Mage but the others will have their own Class quests and I assure you they will be a pain in the butt. The Shaman totem quests suck. The druid quests below 20 are horrible as well.

I guess if you are more concerned about the endgame experience and realize the pain that will be involved you are a tougher person than me!

To your point, though. I always hit most of the starting areas myself anyways. With Horde it is easy to get to all the starting areas (unlike Alliance!). I would just pick one starting area and move your toons there. Do the quests needed then go to the next one and start over. It will take a while but I imagine it will actually help you get to level 10 faster than focusing on one area. I always move my toons to each starting location (except for Tauren area because I hate it) and do those quests. Then I bounce around in the same fashion as I level up.