Here's a tough one to beat for just a little over $500.00 You still need to buy an OS (Operating System) and peripherals (mouse, keyboard, and monitor) as well but you get the idea. http://pcpartpicker.com/p/1rJzT
I am actual more familiar with Intel but you will be hard pressed to beat the price to performance ratio of this particular build. It is very upgradeable as well as your budget increases over time you can upgrade each component as you see fit. Nonetheless, this would be an excellent starting point for a gaming rig. Your particular preferences to be determined as you see fit later. Good luck and have fun with it!