Alright, I'm in a hurry, so I can't go into detail, but...
Get the original Dark sun set. The revised is fine (the felt map is AMAZING), but I like the tone of the original more.
Ivory Triangle set... it really goes into two of the city-states, and it's a great place to run adventures. I've never actually owned it (just a purchased PDF) but it worked great in one of my campaigns.
Veiled Society (or is it Veiled Alliance?). It's about the DS mages, which are great in their own respect, but it also goes into a fair amount of detail about all seven of the city-states. You can base an entire campaign on this one book. It's great.
Buy one monster book, although if you're running a 3e game, you're better off with the Paizo monster stuff (I use it, it's amazing). In any case, the Paizo stuff is pretty good.
"City State of Tyr" is a great place to set your campaigns (it's kind of the Waterdeep of Athas).
***
Don't pick up "Valley of Dust and Fire", since it's pretty much a campaign setting of it's own, set away from the Tablelands - it's an alright book, but not a great intro to DS.
Windriders of the jagged peaks and Mind Lords of the Last Sea are also "mini-campaigns" in that they're set away from the Tablelands, and thus, not worth picking up.
Defilers and Preservers is my least favourite DS book, though - I just hate it.