First, do you have a microcenter near you? use google maps to check. If you do, they have excellent CPU deals atm and I would suggest you purchase your CPU from them.
http://www.microcenter.com/single_product_results.phtml...
This would allow you to get a very well performing system that only breaks your budget a tiny bit.
HAF 912 - 59.99 -Excellent and well priced case. If you don't like the look, there are tons of other choices.
http://www.newegg.com/Product/Product.aspx?Item=N82E168...
7850 - 259.99 - good choice for you budget.
http://www.newegg.com/Product/Product.aspx?Item=N82E168...
8GB GSKILL 1600mhz ram - 46.99 - reliable, cheap and look nice without having huge heat spreaders.
http://www.newegg.com/Product/Product.aspx?Item=N82E168...
Combo Asrock z77 extreme4 with Crucial m4 SSD - 243.98 - excellent mobo with an excellent SSD. You install windows on the SSD and a couple of games. This makes boot times near instant and games load faster. Data and the rest of the games and apps go on the HDD.
http://www.newegg.com/Product/ComboDealDetails.aspx?Ite...
Combo Seagate Barracuda 1TB HDD with Samsung dvd burner - 101.98 - well priced items sufficient for your needs.
http://www.newegg.com/Product/ComboDealDetails.aspx?Ite...
Windows 7 Home premium 64 bit - 99.99 - I can't see any reason you'd need professional or ultimate since they offer no advantage to most people.
http://www.newegg.com/Product/Product.aspx?Item=N82E168...
That comes to $893.56 after shipping from newegg + $149.99 from microcenter.
Soundcards are useless unless you are an audiophile. Modern motherboards come with good ones onboard.
For a monitor you need a 1920x1080 one. If you don't have one, get something like:
http://www.newegg.com/Product/Product.aspx?Item=N82E168...
The 7850 will play almost any game on max. GW2 will play perfectly. If you play BF3, you will need to turn the settings down just slightly (just below ultra).
If you want to break your budget, the gpu could be upgraded to a 670 for another $150. The 670 is excellent "bang for buck" and would serve to future proof the build a bit, though it wouldn't be incredibly useful outside of bf3 currently.
You don't need a cpu cooler if you aren't overclocking. Overclocking is for people who like tweaking to get the most performance out of their hardware. It requires patience and time and gives a decent boost in performance but isn't incredibly noticeable and certainly isn't necessary. If you enjoy tweaking, change the cpu to a 2500k or 3570k and grab the hyper 212+, otherwise don't bother.
edit:
and everything elayman said is correct. Except that you don't need a silver rated PSU, bronze is perfectly fine.
And some info on Ivy VS Sandy (2xxx vs 3xxx).
Ivy gives about a 5-10% performance boot per clock depending on the test. So Ivy @ 4GHz = sandy @ 4.2-4.4GHz.
Ivy gets hotter faster when OCed and requires a more expensive cooler for the same overclocked speeds. But since it's faster per clock, this evens out to them being nearly the same when oced to the limit of the cooler.
So in conclusion: Ivy is better without ocing and Sandy is better with ocing since it's cheaper. There are plenty of exceptions, and I generalized a lot there but that's usually the case.
And this is how to build a computer:
http://www.youtube.com/watch?feature=player_embedded&v=...