I never play games, but was asked to help make an affordable gaming system. Knowing me, I would like to own the high end stuff from a couple of years ago, rather than buy new low end or middle range systems. It probably performs just as well. A gaming rig starts with the graphics card, then you build around it.
Looked at high end video cards, from 2014:
Searched ebay for gtx 770, and found this card for $120 shipped:
http://www.ebay.com/itm/NEW-NVID-GeForce-GTX-770-3GB-198Bit-GDDR5-PCI-Expres-Graphics-Card-VGA-DVI-HDMI-/191849281510?hash=item2cab1bb7e6:g:6QsAAOSw~oFXERUJ (Update: per the review, this is not a gtx 770, so time to search again!)
If you have a PC with a PCI express X16 2.0 slot that this would fit into, it would make for a great DirectX 11 gaming system.
Not much warranty from ebay, or aliexpress for that matter, but at less than half off retail, I don't mind. You have about a month to try out the product, and if it fails, you can get a resolution from paypal (less so from aliexpress, although they work with you regardless). I have consistently gotten my money back, if the product is not what it was supposed to be. It's not hard like wrestling with an insurance company.
Then you would need to make sure of the following: