Cheap graphics cards for bf3?

What resolution are you talking about?

The HD 7750 is the best card under $100 but it's really worth stepping up to $110 to grab the HD 7770 if you want to play BF3.

7770 is best one to play at 1680x1280 and get easily 30 fps + more

^ 1+

Best graphics cards for the money, start here and then shop around.

Also BF3 seems to run slightly better on Nvidia cards

http://www.tomshardware.com/reviews/gaming-graphics-car...

^^ true but Nvidia doesn't have any good options below the GTX 660 which is over $200

7770 ditto it is unchallenged in the budget sweepstakes.

GTX 560 http://www.newegg.com/Product/Product.aspx?Item=N82E168... is highly recommended, if not get the GTX 550 Ti http://www.newegg.com/Product/Product.aspx?Item=N82E168... it's still OK though at medium-high settings.

^^ Wow both of those are utter crap recommendations. The 7770 is 20% faster than the 550ti for $10 extra. The 7850 is 20% faster than the 560 for $15 extra.

This GTX 570 is the only Nvidia card currently recommendable below the 660:
http://www.newegg.com/Product/Product.aspx?Item=N82E168...