Well, building one yourself will be, by far, the cheapest route to take. And should yield you a higher performance machine than anything you could buy pre-built. A mid-range price option would be to go somewhere like
ibuypower, where you can specify all the components you want, but they send it to you already built.
If you build yourself, you can actually get away with closer to $550 for something that will run pretty strong. The biggest budget breaker (and gaming performance indicator) is the graphics card. You could skimp a bit on the graphics card for now, and then go back in a year or so and pick up a $200-300 graphics card to replace a lower-end model, and really boost your gaming performance.
I actually just found this, which looks to be a reasonable option at the $570 price point, already built:
http://www.tigerdirect.com/applications/SearchTools/item-details.asp?EdpNo=4959029&Sku=C477-G1410This all assumes you have a monitor you can use. If you need one of those, too, add $100-150 to the price.