There isnt much you can accomplish with 300$ unless there are big sales. If oyu want good 1080p gaming you would have to spend 400+ for cpu+mobo+graphic card. Unless you can find used parts.
My suggestion is a i7 2600k, a cheap p67 board if u can find one and a gtx 560 ti (around 200-150$)
If you can spend abotu 300+ for just graphics card alone, then get gtx 480 sli. It consumes abit of power but it nearly as strong as a 670.