Like the tittle says what should i buy first, but also the other problem is i don't have my new computer yet and i well be getting it july 3rd so should i wait or buy dawn guard right when it comes out for the Xbox.

Well I'm on xbox but if i was in your position I would wait because then you would end up buying it twice.

Depends on how patient you are. Since you asked which to buy 'first' you are apparently planning on buying both anyhow, so unless you want to eventually have a PC version of Skyrim without Dawnguard waiting makes the most sense unless you are rabid enough over playing it now to buy it twice.

As there will most likely be mods that incorporate some of the features of Dawnguard, I would recommend waiting, so you don't end up buying Dawnguard twice.

I will be incline to agree with BS and Morchai, here.