For $850? I doupt that you'll be able to get Ultra in Ultra for that, half of that would be needed just for a card to run in ultra (Comparing with BF3) Your best bet would probably get onto Ebay and use your money there, you'll be able to get a better system for your money.
At minimum I think you need to be looking at GTX 560Ti, 6950, GTX 570 or 6970 in order to play all newer games in all their High-def-Glory.
I'd also recommend avoiding AMD build and try to squeeze an i5-2500k into the build.
Not sure how close to $850 you could make this but somewhere along the lines of:
Z68 motherboard $120
4GB DDR3 1600Mhz CL9 1.5v RAM $30
HDD 7200RPM $80-140
Mid-Tower-ATX case $60
Aftermarket CPU cooler (although not "necessary" right away) $30
GTX 560Ti or 6950 $250
500w PSU (Antec, Corsair, XFX or SeaSonic branded) $80
For what your wanting to do AMD will be best for you with a budget. Im using a 965BE not even touched its clock and BF3 runs fine with it on maxed settings with my GTX580. Intel works best if you have the money and more for professional uses. But for gaming, cheep AMD does perfect.