Mantle sucks ass IMO, only a few games support it and Mantle only improves the peformance of low end AMD GPUs, the higher spec your AMD GPU is the less peformance increase you get with Mantle.
Now as for your thoughts on how to run Mantle, you only need a AMD GPU, no need for a AMD CPU.
But instead of getting something low end and then relying on Mantle to have a playable enjoyment out of your games, get something that is actually good and worth your money.
The 750Ti fits your budget perfectly and will run most demanding games at an acceptable framerate of 30 or higher at very high settings, however i do recommend you to get a non reference model.