Upgrade the CPU and VC . I believe you maybe able to unlock a dual of triple core Athalon II or Phenom II with that MB, although please double check that before you buy anything. I would think a 955 and a 5770 would be a good upgrade for you. Is your PSU OK?? By OK I mean major brand, Corsair, Antec, Seasonice, OCZ etc. and 550 watts or more.
According to Gigabytes' page here it supports the new AMD Phenom™II X6 processors. Check the page and your board to be sure but I would buy that at Newegg here for $180. Of course you can shop around for a better price This is just an example. So that leaves $120 for a video card. So lets try a MSI R5750-MD1G Radeon HD5750 1GB PCI Express 2.1 x16 Video Card for $134! I suck at sticking to a budget Or maybe a Sapphire 100283-3L Radeon HD5770 1GB GDDR5 PCI Express 2.0 Video Card for $144 after mail in rebate. Both of these cards have the resolution you're looking for. They both only take a single power connector so you have plenty on your psu. So if you have a preference as to brands we can look some more. Are these choices maybe what you were looking for? I would definitely get for the best processor first then work on the video card next. Whatcha think? Or if you don't mind used and shop ebay here is that processor for only $145 buy it now - but you only have 1 day 18 hours (Nov 19, 201011:11:50 PST). And here's a great buy, NEW only $135 with shipping for the Sapphire Technology ATI Radeon HD 5770 1 GB 100283-3L. And you got 3 days.
I recommend the Phenom II X4 940 TBH. The X6's are cool, but on your budget, not needed. There good, but at your budget and since you want to play games. From X4 to X6 the gaming performance is no different so you could save 80$ by going with the 940. Plus the 940 is a great CPU for budget upgraders on the AM2+ platform.
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.
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.