My suggestion is to go with the i5-3570k and an appropriate Z77 mobo which allows for overclocking. I would not overclock without saving up money for a 3rd party heatsink. The total cost is $342 which includes shipping.
If you use a Quick Sync compatible video encoding program like Espresso and one of the 3 supported codecs (H.264, VC-1, MPEG2) then Quick Sync encoding is extreme fast. Without using Quick Sync you probably need a Core i5/i7 overclocked to 9GHz - 10GHz to match Quick Sync's speed. Of course those clockspeeds are impossible.
If this is a strict $300 max build, then following will cost you $270. You must use the Coupon Code for the $15 off on the i5-3570 CPU.
You've got $300 to spend for a compatible MOBO, CPU, and GPU with the intension of video encoding!
Save more money to get something competent. In a world of pay-day loans, living beyond our means and living on credit, and buying lesser components only to completely waste the money away by junking them to upgrade them later, you wonder why the economy is collapsing?