Looks like a pretty solid build, yet if you plan to overclock in the future, you are definitely going to need an aftermarket cooler for that i5, since they run hot compared to the older models.
If you just want to keep the build at stock right now, and overclock later with an aftermarket cooler, that would be idea for your budget, because then you wouldn't have to subtract from your graphics card budget for the cooler.
As for the graphics card, if you still want to spring for the 6870, then go for it. Its a great card, my buddy has one. Plays everything he wants at the highest it goes.