Here's a similar build that uses slightly different parts (ones that I would trust). The main changes are a dual channel RAM kit for about $7 extra (worth it) and the lowest price PSU I could find from a manufacturer I have heard of and trust.
Total Cost = $635.43 after discounts and postage.
http://pcpartpicker.com/user/Falkerz/saved/3wxY
Here's an AMD build. Notable changes are a Quad core chip for $10 extra, an ASRock mobo for $12 extra (it has 4 RAM slots and decent reviews).
Total cost = $657.45 after discounts and postage.
http://pcpartpicker.com/user/Falkerz/saved/3wyl
Again, these are just my suggestions. The build you've specced up will work well for web browsing, flash games, pre 2011 ish games (in my opinion) and movies. I would encourage more than a dual core chip if you want to play new games, but newer games may well run on your system (no guarantees of course).
I'd still go with the 7870 given your budget, it should be able to handle that. The performance between a 7870 and 270x is similar. And like others have said i wouldn't get the 4gb 270x, its not worth it because the card won't be able to utilize it Unless you want to crossfire two of them which I actually hadn't thought of before.