At high 1080p a Q9550 will make BF3 stuttery even on lower settings.
I was running a Q9550, 6GB RAM with a GTX470 (pic-e 1.1 x16), on low settings @ 2048x1152, v-synch'd to 60fps, but it didn't feel smooth on heavily populated maps especially heavy small maps. It did get better if I lowered the resolution, not ideal for me though, should work for you though.
Upgraded to a 3570k, and its much smoother, so I'm not convinced that the core 2 quad is enough.
Have you factored in cash for selling your current components.
Don't bother with win 7 pro, home premium 64 is enough.
edit 2, didn't notice that the other replier was quoting from newegg which doesn't help you. For 220, you are a little stuck especially throwing windows in there as well. 2nd hand q9550's will be available (mine included), but you are really tight on budget, in fact i'd leave the CPU alone for now.
i3 will suffer a tad more then the 2500k or 2600k in multiplayer but i a lot better then the cpu that you want to get. sorry
also that 250 includes a 6850.... not sure why you thought it doesnt.
bottom line is the build i showed you is much better then the one you want to get. by a lot!
Im sorry, i didnt look at the 6850, silly me . But i got this pc for my 13th birthday (Im 13) and my dad put alot of money and effort into it, so i don't want to just throw it away and make a new one, because i think it would look ungrateful and rude after all the effort he put in. But he is fine with me upgrading it, so please could you recommend the top end parts i could upgrade a socket 775 with and also the best graphics card for up to £80 ($128)