Dont expect high settings in BF3 on this rig, need a bit more cash for that. You better have a spare windows key, because at this budget, including that will be the difference between an entry level graphics card or none.
For BF3, you'd be better off with an Nvidia card, they can handle BF3 better, particularly on the lower end. But yea, ManofChalk has a good foundation for a build. The budget you have is pretty low though. The call of duty games and WoW won't care very much about the video card.
I'd recommend stepping up to a 7850. Even with Nvidia's moderate advantage in that game, the 7850 still beats all of Nvidia's cards in its price range significantly except for the far hotter and louder GTX 480 which kinda sucks if you don't give it an aftermarket cooler to keep the heat under control.
A cheaper case, PSU (no need to spend $75 or so on a mere 500-600w PSU), and getting the Phenom II x4 830 instead of the 965 (overclocking blurs the performance difference quite well) should make room for the 7850. If not, well, you could get a far cheaper motherboard without any problems.
Then again, it's all personal preference. I don't mnd getting a Corsair PSU (still high quality), a Rosewill case (still high-quality, but probably not quite as nice), the cheaper CPU, and even a cheaper motherboard to get a far better graphics card. If you're getting a quad core Phenom II CPU, then you might as well give it some performance headroom to work with on the graphics side. Get is a decent $20-30 CPU cooler and I'd be quite happy with it as a gaming rig.
The 7850 is a heck of a lot faster than the 7770 and an overclocked Phenom II x4 can make good use of that, even in BF3. It isn't until games such as Batman AC that the Nvidia cards have a serious lead and even then, it's counter-able with AMD's cards having such lower prices after the latest price cuts. I'm not saying that going with Nvidia wouldn't make someone happy with their choice, but I prefer more performance for the money, especially when it concerns effects such as AA.
EDIT: You might actually want to go with the FX-6100 in this case. It's not much more expensive than the Phenom II 965 at all and would offer much better online performance in maps with around 40-64 players (estimating, but close enough).