Do quests for each faction until friendly, it opens up most zones as well. You should do this first, you get decent quest rewards and there is no reason not to hit friendly and get tabards first. The only exception I think might be Violet Hold, no quests afaik (even still I had a violet hold tabard on everyone, not sure how? Maybe just turning in daily heroics?)

After that I really wouldn't sweat it too much, I'm exalted on all 4 factions and I run maybe 1-2 heroics a day max, many days none. I haven't done most of the quests in icecrown/SP/Sholozar/Howling/Borean, just the starters. Just pick a few heroics you find easy (most will probably say Gundrak, Drak Keep, Utgarde Keep, maybe Halls of Lightning, Violet Hold and Stratholme) and farm them daily, most should have drops off the last boss that will last you a while.