http://www.cyberpowerpc.com/ seems to have okay prices on AMD gaming PCs.
Alienware X51 Ubuntu Gaming PC cost $599 at
http://www.alienware.com/ubuntu/ because you don't need to buy Windows since it uses the free Ubuntu OS which works with Steam for Linux, playing Linux games, and playing Windows games with WineHQ, and PlayOnLinux.
You'll save money by building your own Gaming PC, but you need to put it together yourself, buy(if you choose Windows over Free Linux OS) and install the operating system, and software yourself which can be hard for beginners, but there are many tutorials on YouTube and other sites for building computers.
If you already have a pretty good PC with a Multi-Core 2.0-4.0 GHz CPU, 4GB or more RAM, PCI-Express x16 expansion port, and a 500W or higher wattage power supply, you may be able to just buy a Nvidia Geforce GTX 650 video card, and play many PC games from Steam, and other PC games from different companies.
Most games on Steam tell you the minimum, and recommended system requirements at the bottom of the download page.
You can also use
http://www.systemrequirementslab.com/cyri to see what games your computer can run.