To build a cheap gaming PC, you should spend more on the graphics card, for other parts get the cheapest you can get, you will be able upgrade to a better one later if you have the budget.
Here is one of the build under $500 with i3 processor and powerful graphics card:
If you can get Skylake or i5 you should get it, but since it is more expensive we will choose a Haswell CPU and a i3. The total price doesn't include Windows OS, you will have to buy it for about $100 if you want to use it. If you have old version of Windows and it is not OEM version, you can use it.
Edited by batman1234, 12 December 2015 - 08:32 AM.