For your needs, I also suggest an APU*.  Go with the Brand New A10-7850K.  The GPU is integrated with the CPU, so no additional costs there.  Spend the discrete GPU money on the largest SSD that fits in your budget.  You can always add a GPU at a later date if you decide you want more performance, which is much easier than adding a SSD later.   
Here ya go: http://pcpartpicker.com/p/2Zdx3   
Add THIS RAM. It's not an option on PC Parts Picker.  But it's nice and fast to benefit the integrated Radeon R7.   
*Normally I'd recommend a quad-core i5 at a minimum, but it puts a build out of budget, and beyond required performance.   
Edit: Don't forget you also need to budget for a monitor, mouse, keyboard, speakers, and an OS.  Windows 8 can be had for around $100.  Ubuntu and SteamOS are free, but may not work with your game.