With that low of a budget, just being real with you, you are forced to go with AMD CPU. and thats not bad! It will leave more money open for a better graphics card leading to more FPS. don't expect to get better FPS if u buy an intel cpu when ur budget left will be very low for the graphics card. your average Intel cpu compared to it's "related" AMD CPU will only give about 15% better performance and it will be worth twice the money.
This is a fact, amd cpu will get you more FPS because of the better Graphics card u can buy with the money saved.