Questions from a first time computer builder.

Processor- intel i5-3570
Get the "K" version and you can OC it if it starts to be too slow.
http://www.newegg.com/Product/Product.aspx?Item=N82E168...

motherboard
Get a z77 LGA 1155 intel board, with enough pcie 3.0 slots for your graphics card.
z77 overclocks. H77 does not.
http://www.newegg.com/Product/Product.aspx?Item=N82E168...

graphics- geforce 660 gtx
You will be good for a while.

RAM.
8gb at 1600mhz is the standard. 16gb might give you 2-3 more fps in most games.

PSU
Corsair TX is good
http://www.newegg.com/Product/Product.aspx?Item=N82E168...

Windows
8 if you like metro and 7 if you don't.

hard drive- barracuda 1 tb

Good

Case
HAF 912, is the best budget case IMO. Comes with 2 fans, upgradable to 8 fans, has great airflow, and cord managment.

http://www.newegg.com/Product/Product.aspx?Item=N82E168...

You won't get all high settings for 3 years. 3 years from now, your card will be the age equivalent of a 460. Which is a good card, but it is far from all high settings. So you will still be medium to high settings in three years, maybe a little higher maybe a little lower. the 3570k is the strongest not i5 out there, you'll be fine with that for a while
with that cpu. Get 8gb ram. For your gpu, look into getting a 7870, it's stronger for usually the same price. You also need a psu. If you want to ccfx in the futur get a 700w, if not a 550 is fine. Get a z77 motherboard. for cfx get an asrock extreme 4 z77, if you don't want to a pro3m. For case, just get what you think looks nice, make sure it is atx if you get an atx motherboard though.

the only thing i add is make sure you pick up a evo 212 after market cooler. there better then the stock intel platic unit that comes with the cpu there about 20-30 online. when you buy your ram buy ram that is low profile or has small heat fins.if in the feature the evo cant keep up with your overclock and you need to replace it with a bigger cpu cooler the ram will fit under the larger coolers. with case shopping be care full not all case can take all gpu cards and heat sinks. do to the case length and where the hard drive tray is some cases can only take 9 inch cards..some 10 inch other can take the extremely long cards.
with cpu coolers it depend on the case with for the max cooler height and if there a fan on the side panel.

I'll second this suggestion and also recommend the Corsair 200R: http://www.newegg.com/Product/Product.aspx?Item=N82E168...

For $700 - $800 I'd suggest cutting back on the CPU and motherboard and getting a better GPU:

PCPartPicker part list / Price breakdown by merchant / Benchmarks

CPU: Intel Core i5-3350P 3.1GHz Quad-Core Processor ($179.99 @ Newegg)
Motherboard: ASRock H77 Pro4/MVP ATX LGA1155 Motherboard ($87.55 @ Newegg)
Memory: Corsair Vengeance 8GB (2 x 4GB) DDR3-1600 Memory ($49.98 @ Outlet PC)
Storage: Western Digital Caviar Blue 1TB 3.5" 7200RPM Internal Hard Drive ($73.98 @ Outlet PC)
Video Card: PowerColor Radeon HD 7870 XT 2GB Video Card ($239.99 @ Newegg)
Case: Corsair 200R ATX Mid Tower Case ($52.99 @ Microcenter)
Power Supply: Corsair Builder 600W 80 PLUS Certified ATX12V Power Supply ($49.99 @ Newegg)
Optical Drive: Lite-On iHAS124-04 DVD/CD Writer ($17.99 @ Newegg)
Operating System: Microsoft Windows 7 Home Premium SP1 (OEM) (64-bit) ($89.98 @ Outlet PC)
Total: $842.44
(Prices include shipping, taxes, and discounts when available.)
(Generated by PCPartPicker 2013-02-16 19:36 EST-0500)

Without Windows the build is $750.52