I recommend the Phenom II X4 940 TBH. The X6's are cool, but on your budget, not needed. There good, but at your budget and since you want to play games. From X4 to X6 the gaming performance is no different so you could save 80$ by going with the 940. Plus the 940 is a great CPU for budget upgraders on the AM2+ platform.
940 96$:
http://www.newegg.com/Product/Product.aspx?Item=N82E16819103644&cm_re=940-_-19-103-644-_-Product
This is also a great OCer since its a BE cpu. So... I recommend sticking a 25$ into the budget and getting this CPU cooler, unless you already have one, but the HSF I rec is the Hyper 212+.
Hyper 212+ 26$:
http://www.amazon.com/Cooler-Master-RR-B10-212P-G1-Universal-Heat-Pipe/dp/B002G1YPH0/ref=sr_1_1?ie=UTF8&s=electronics&qid=1290042546&sr=8-1
Now for GPU suggestions.
I recommend the GTX 460 or the 6850 because the resolution your at needs a stronger GPU imo. The 5770 is good, but just not good enough for Bad Company 2. I'm telling you right now, BC2 is really graphic intensive. I use an 5850 OC to 5870, and it still lags on FPS a bit on ALL high settings and AA 8x. The 6850 and 460 are OC beasts, they perform great and are DX11 supported. Umm... The 460 is good because with a little clock tweak gets it up between 5850 and 5870. The 6850 is a great OC and OC's up to the same performance as the 5850/5870. Also, like the 460, has low power consumption.
Anyway... Here are GPUS.
MSI 460 Cyclone 768mb 170$, 155$ after MIR:
http://www.newegg.com/Product/Product.aspx?Item=N82E16814127512
768mb to 1gb is not difference unless you leave it at stock, but the Cyclone OC's like a beast and since you have great airflow (Antec 300) then there is no prob. But... If you have terrible cable management, then I defiantly don't suggest this blower design.
The best 460 hands down is this: MSI 460GTX Hawk 1GB 210$, 190$ after MIR:
http://www.newegg.com/Product/Product.aspx?Item=N82E16814127518
OC's like a beast, Freaking cool too... Get this if your getting a GTX 460... Plus it's stock OC'd if you don't want to OC yourself.
BC2 review for the Hawk, check out the Overclocking section of that review:
http://www.techpowerup.com/reviews/MSI/GTX_460_HAWK/7.html
The 6850s... Love em.
Gigabyte 6850 1GB 190$:
http://www.newegg.com/Product/Product.aspx?Item=N82E16814125348&cm_re=6850-_-14-125-348-_-Product
Great card, great company, OC's good too and runs cool.
Best 6850 is this card: Asus DirectCu 6850 1GB 200$:
http://www.newegg.com/Product/Product.aspx?Item=N82E16814121399&cm_re=6850-_-14-121-399-_-Product
Review Directcu 6850:
http://www.techpowerup.com/reviews/ASUS/Radeon_HD_6850_Direct_Cu/7.html
Not stock OC'd soo... Performance won't seem as good as the Hawk. But go to the Overclocking section and you'll see how great this card OC's.
Overclocking for Hawk and DCU:
DCU:
http://www.techpowerup.com/reviews/ASUS/Radeon_HD_6850_Direct_Cu/31.html
Hawk:
http://www.techpowerup.com/reviews/MSI/GTX_460_HAWK/31.html