Just go on craigslist or ebay and find something cheap. You get probably get something with a dedicated GPU in it and probably run games on low settings for like $200.
Rpi does require you to buy a micro usb for power, as well a micro SD for storage. It's not as cheap as just buying the device. however, it probably would still be cheaper than everything else, I was just under the impression we were looking at actual functional desktop. I could be wrong but I don't think you can install other os on them.