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.