Here's mine. Didn't include keyboard, mouse, optical drive, etc.
http://pcpartpicker.com/p/R6xN99
Pentium G3258
R7 260X
MSI H81M-P33
Antec 300 Case
Corsar CSM 450W PSU
Kingston Fury 1x4GB 1866MHz RAM.
Should have okay gaming. Total price is ~$290 but that's after rebate. There is a Gigabyte GTX 750 on sale right now too so you could replace the 260X with that but I believe the 260X would be stronger. Honestly if you can get a second hand computer case, keyboard, mouse, and monitor for free or have old one to reuse it would free up your $300 budget for the core components.