I wouldn't get an FX processor. They solve the issue of not having as high performance as Intel by adding more cores, which not many games are going to even utilize 8 cores.
Also, get an R9 280 instead, roughly the same performance for a lower price. Use the saved money to get a better CPU and PSU. Don't skimp on the PSU, it's a very important part, and the Corsair CX series is a budget series, they're really not quite as great as people make them out to be. Get a Seasonic perhaps?
Do you know what you're doing for an OS yet? It's not included in that build.
Here's a good build in your price range, I think. Includes windows too. I do suggest getting a better PSU though.
Edited Champions build further, this should be as good as you can get for your needs and budget.
http://pcpartpicker.com/user/Tokthree/saved/VJkH99
6000th post! :D