For $850, you can build a pretty decent gaming rig.
I'd go for the following:
i5-3570k ($200)
AMD Radeon 7950 ($300) (about the same as 660 ti at stock clocks, but overclocks WAY better)
Any z77 mobo ($100) will work generally, find one for cheap, and before buying, look up some reviews of the board. I got my i5-3570k to 4.6 Ghz with a Hyper 212 plus ($30 air cooler). And I used the CHEAPEST z77 board I could find, even though the reviews generally sucked for it, I used the MSI Z77A-G41.
Hyper 212 Evo ($30)
8 Gigs of corsair, Kingston, gskill, or mushkin ram ($45)
Adata sx900, Kingston hyperX 3k, vertex 4, crucial m4, Samsung 830, or Samsung 840 pro 120/128 GB SSD ($100) get the cheapest
Get a corsair, seasonic, or xfx PSU (good from my experience and other reviews, not to say others are bad) 550-750 watt ($50-$80)
I know that it is above $850, however, I posted regular prices, look for sales and buy only if you get a somewhat decent deal, regular prices are BS, don't get ripped off. I got my mobo for $75, 8 GB ram for $30 128 GB SSD for $70 hyper 212 plus for $15, GOOD DEALS ARE OUT THERE!
Good Luck.