Almost any computer you can build with parts available today including a reasonably powerful GPU will run current games at or near max settings because PC games are dummed down so as to be able to run on 5 year old consoles. Let's hear it for the consoles.
Intel Core i5-2500K (You don't need an i7-2600 for gaming as it has zero performance benefits in that aspect.)
ASUS P8P67 (You can afford it after dropping the i7 for an i5.)
G.Skill Ripjaws X 8GB 2x4GB 1600Mhz DDR3 (You will save yourself some upgrading later, and since this kit can be found at ~70$ I don't see why not)
The 6870 is fine, but Sapphire is preferred brand over XFX when it comes to graphic cards. Also consider getting an eVGA 560 (Non-Ti) for the lifetime warranty offered by eVGA.
Aerocool is NOT a reputable PSU brand. You do not need 700W for that build, more like 500W. I suggest a Corsair CX500 V2 for ~50$.
Hitachi is also known for their failing Deskstar line. Try the Samsung Spinpoint F3 1TB for ~65$ or the WD Caviar Black 1TB for 80$ which I would recommend.