I have a 6790 and i play BF3 at 1680x1050 with everything on ultra; I dont play with any AA though no post or defered and I get 40-60 FPS with it idling around 40 when there is alot going on; on screen.
at that screen resolution the gts250 you have should do you fine. nothing under $100 will get you much better fperformance. your mostly limited by your CPU. Upgrade the cpu before you do anything else. and some more ram would be good.