I don't understand why people just look at processor and ignore other components especially in a gaming build.
At 3-4K u won't get a mobo with USB 3.0. USB 3.0 is so common nowadays. Even a non-techie can feel the difference between USB 3.0 and USB 2.0 speeds. Other feature is SATA III. Although not much useful for HDDs but it's a necessity for SSDs. There's a little overclocking feature in this mobo also but not recommended to overclock on this mobo
A good cabinet will cost atleast 2.5K
The GPU is the primary concern in a gaming build. Everything changes with the GPU. The 5770 is way underpowered for a CPU like FX 6300. The recommended option is a GTX 760 that cost 20K. GPU alone exceeds your budget
Here is an example budget balanced gaming build:
http://www.tomshardware.com/reviews/build-a-pc-fx-6300-overclocking,3617.html
It's a 18 page article, everything is explained