your build right now looks actually, really solid. only thing i would suggest is that since you originally wanted about 1000$ computer, you should get a cheaper case.... 160$ for a case is alot of money.... i feel that the one Nightfox suggested is better since its cheaper and is also very good.
the 6970 is a good graphics card but most enthusiasts prefer to buy the 6950 because you get more bang for your buck. its not as good as the 6970 but it is atleast 40$ cheaper. the prices range from 260$ (today only(?)) ~ 300$ compared to the 340$
and yes, its fast.