Build a gaming pc for $700 budget

CPU: Intel Core i5-3470 3.2GHz Quad-Core Processor ($184.99 @ Amazon)
http://pcpartpicker.com/mr/amazon/intel-cpu-bx80637i534...
Motherboard: ASRock H77M Micro ATX LGA1155 Motherboard ($69.99 @ Newegg)
http://pcpartpicker.com/mr/newegg/asrock-motherboard-h7...
Memory: Mushkin Blackline 8GB (2 x 4GB) DDR3-1600 Memory ($35.57 @ NCIX US)
http://pcpartpicker.com/mr/ncixus/mushkin-memory-996995
Storage: Western Digital Caviar Blue 1TB 3.5" 7200RPM Internal Hard Drive ($69.99 @ NCIX US)
http://pcpartpicker.com/mr/ncixus/western-digital-inter...
Video Card: Sapphire Radeon HD 7850 1GB Video Card ($164.99 @ Newegg)
http://pcpartpicker.com/mr/newegg/sapphire-video-card-1...
Case: Antec Three Hundred Two ATX Mid Tower Case ($57.73 @ NCIX US)
http://pcpartpicker.com/mr/ncixus/antec-case-threehundr...
Power Supply: Antec Basiq Plus 550W 80 PLUS Certified ATX12V Power Supply ($59.99 @ Newegg)
http://pcpartpicker.com/mr/newegg/antec-power-supply-bp...
Optical Drive: Lite-On iHAS124-04 DVD/CD Writer ($17.89 @ Outlet PC)
http://pcpartpicker.com/mr/outletpc/lite-on-optical-dri...

Total: $661.14

You can replace the 7850 with 7870 if you want to.

I would make every effort to use a wired connection over wireless. It will be faster and more reliable, slow network speeds are incredibly annoying for games.

That above build looks great, I'd aim for a better quality PSU though. A decent PSU is important for good system stability. That Antec one is OK but you can afford a better one.

i5-3470
2x4GB Crucial Ballistix Sport 1600Mhz C9 1.5v
ASRock B75M-DGS
MSI Twin Frozr HD 7850 2GB
Seagate Barracuda 500GB 7200RPM
SeaSonic S12II 430B 430W
Fractal Design Core 1000
LD DVD Burner
ASUS PCE-N15

Total - $703.91 before shipping and rebates

The 2GB GPU should last a bit longer and the higher quality PSU should allow for better stability. Does have a smaller HDD and case though.