A guildie last night just achieved Exalted status with the Horde Expedition and was looking to who's tabard they should Champion first?
When I started championing the different factions, I started with Knights of the Ebon Blade, because they had an item that I wanted as an upgrade the quartermaster sold. Unfortunately, by the time I reached exalted, I had already found a better upgrade by doing heroics.
That's why I suggest that the first tabard you start wearing is not for the gear, but for the vendor savings. I am always in Dalaran; my hearth is set there. I do my repairs, I pickup reagents, I buy food and drink there. Heck, I even bought my final 2 mounts for the Leading the Cavalry achievement there. By reaching exalted with the Kirin Tor, I have saved myself a lot of gold for all these items. In addition to the vendor discounts (20% at Exalted, 15% at revered, 10% at honored). I purchased the Armored Brown Bear at Honored for 750g, if I waited until Exalted, I could have purchased it for 600g. If you play a caster, I suggest you pickup the head enchants at revered.
After that, (IMHO) I'd champion the faction that is the furthest from reaching. :) You will get rep by doing the quests chains in each area, plus some over-flow rep by doing related quests.
Install an addon like Minimalist, which (among other things) announces your remaining rep with each kill.
Ok, back to grinding Hodir rep, need that better shoulder enchants.