Here's the PC I currently use. It's right within your budget. You didn't list any specifics so brands and case selection are influenced by my own personal taste:
Maxes out just about every game @ 1080p. It's also small-sized for portability.
If you run at higher resolutions then you'll probably want a beefier GPU. Or if you do lots of work like video editing, CAD, and the likes, then you'll probably want to upgrade to a 4770K. Also, this build assumes you plan to overclock. If not you can get away with a non-K CPU and an H87 motherboard.