Look up a used Dell Optiplex 790, you can usually find these for cheap (around $100) and they come with an intel i5 2400. With this, you can also invent into a slim gtx 1050 (about $150), this should handle most games pretty well.
All in all, a pretty good gaming pc for, give or take, $250! Let's say $300 just in case.
(315 - 375 aus)