If you plan to play WOW mostly then the 5870 is a massive overkill. Get the 5850 (like me- I am a WOW player also and will buy it and a 26" monitor) and a good 500+ W PSU and be done with it. Keep the rest of the money and get your girlfriend/boyfriend something nice for Valentines.
PS. AA is a method of smoothing the edges in images. More AA, more smooth the image is. The 5850 will handle AA beautifully in WOW and other games (except Crysis of course)