I5 3570k and Radeon HD 7870(2GB) build under 600?

First off thanks in advance for all help. I'm not a big pc gamer but I want to change that. I like eye candy but keep in mind I'm coming from a Xbox 360 so it probably won't take much to impress me. I have done my research and I was wondering if it was possible to get the i5 3570k cpu with the Radeon HD 7870(2GB) for under 600 seeing as those seem to be the go-to parts when on a budget. I won't need an OS, or a monitor. I think I could squeeze out 650 if need be. I saw this posted on the 600$ marathon comment section and it looked good to me(First time builder) except for the processor. Everyone around here seems to down the AMD's in favor of the Intel chips so that's why I'm skeptical.

PCPartPicker part list: http://pcpartpicker.com/p/Gfx8
Price breakdown by merchant: http://pcpartpicker.com/p/Gfx8/by_merchant/
Benchmarks: http://pcpartpicker.com/p/Gfx8/benchmarks/

CPU: AMD FX-6300 3.5GHz 6-Core Processor ($119.99 @ Microcenter)
Motherboard: Gigabyte GA-970A-DS3 ATX AM3+ Motherboard ($77.55 @ Newegg)
Memory: Corsair Vengeance 8GB (2 x 4GB) DDR3-1600 Memory ($49.50 @ Newegg)
Storage: Western Digital Caviar Blue 500GB 3.5" 7200RPM Internal Hard Drive ($39.99 @ Microcenter)
Video Card: PowerColor Radeon HD 7870 XT 2GB Video Card ($239.99 @ Newegg)
Case: Zalman Z5 ATX Mid Tower Case ($25.98 @ Newegg)
Power Supply: Corsair Builder 500W 80 PLUS Bronze Certified ATX12V Power Supply ($29.99 @ Newegg)

Total: $579.48