http://www.tomshardware.com/reviews/build-a-pc-fx-6300-overclocking,3617.html
This might be a good place for you to get started, the build there is $650(which is SLIGHTLY over your budget) but it looks pretty good. Also you won't have to purchase a case so it should suit you pretty well.
"
Component Model Purchase Price
CPU AMD FX-6300 $120
CPU Cooler AMD boxed heatsink/fan 0
Motherboard MSI 970A-G43 ATX $70
RAM Kingston HyperX XMP Blu Red Series KHX16C9B1RK2/8X 8 GB (2 x 4 GB) DDR3-1600
$57
Graphics EVGA GeForce GTX 760 2 GB 02G-P4-2760-KR $250
Hard Drive WD Blue WD10EZEX 1 TB $57
Case NZXT Tempest 210 CA-TP210-01 $40
Power Antec VP-450 450 W ATX12V v2.3 $40
Optical Samsung 24x DVD Burner SATA Model SH-224DB/RSBS $16
Total Price $650"
(I'd just snap a screenshot for you but I'm on a school computer without puush)