Your budget is a tad low, if you can increase your budget to about $450 USD, it's definitely doable. I would recommend a AMD APU-based PC for WoW. You should be able to run it up to [1920 x 1200] resolution w/ medium settings while getting desirable frame rates.
**While there are cheaper options out there, the price to storage + performance ratio are lacking. The WD Blue 1TB is a solid choice because it offers amazing price to storage ratio while having solid performance and durability.
****I HIGHLY recommend you getting this aftermarket cooler for your APU because it's your biggest asset (CPU + GPU in one). Having it run cooler will positively affect almost everything you do while extending it's lifetime.
Hope this information helps.
Coffee~
EDIT: The above build comes to a total of $422.89 USD Total before taxes.