I came up with this. FX-6300 w/ OC'able Mobo, 4gb RAM, And 21.5in, 1ms response time, 1080p, 60hz monitor.
You didnt specify if you cared for monitor size so I just put that theres another that stays within budget that it 27in as well but has a 5ms response time.
http://pcpartpicker.com/p/WhBRYJ
EDIT: if you dont want to bother with the BIOS Update with the 970 board theres also this. No BIOS update needed and still OC'able as well
I]http://pcpartpicker.com/p/XXF6pg