Budget Gaming Build Help

[machinations]

Hiya guys, This is my first time building a PC. Im working on a cheap gaming PC, my price range is about 450-500$ These are some of the parts i've picked out

MoBo: MSI ZH77A-G41
RAM G.SKILL 8G(2x4G) DDR3 1600
GPU: Sapphire HD6570 1G GDDR5
CPU: Intel i5-3470
Power Supply: Antec vp550 500w

Will these parts work? Do you guys have better suggestions?

Do I need to buy a cpu cooler? I thought Intel chips came with a cooler in-box. I dont know though.
Thanks in advance guys.

 

[machinations]

Here you go: http://pcpartpicker.com/p/1D4k2

CPU: AMD FX-6300 3.5GHz 6-Core Processor ($117.98 @ Outlet PC)
Motherboard: Asus M5A78L-M/USB3 Micro ATX AM3+ Motherboard ($44.99 @ Microcenter)
Memory: Kingston Blu 8GB (2 x 4GB) DDR3-1600 Memory ($54.99 @ Newegg)
Storage: Western Digital Caviar Blue 500GB 3.5" 7200RPM Internal Hard Drive ($54.98 @ Outlet PC)
Video Card: MSI Radeon HD 7790 1GB Video Card ($123.98 @ Newegg)
Case: Zalman Z9 Plus ATX Mid Tower Case ($39.99 @ NCIX US)
Power Supply: XFX 550W 80 PLUS Bronze Certified ATX12V / EPS12V Power Supply ($44.99 @ NCIX US)
Optical Drive: LG GH24NS95 DVD/CD Writer ($15.98 @ Outlet PC)

Total: $497.88
(Prices include shipping, taxes, and discounts when available.) (Generated by PCPartPicker 2013-09-12 20:29 EDT-0400)

Hey, thanks so much for the answer
Wow, I did not realize how much cheaper AMD cards where. Its half the Price of the i5....
Will this build be able to run recent games? I'm not looking for super-ultra 1080p stuff, I just need a pc that can run games without crashing.

 

[machinations]

Could I replace the GPU you suggested with a Saphire/Radeon HD 7770 2G DDR5. As I live in china, sometimes I cant find the exact parts I need.

 

[machinations]

Thanks so much for your answers again 😀