You should absolutely go for the FX-6300 and overclock that sucker. The GIGABYTE GA-970A-UD3P
is a good overclocking board, and it's just the right price for your budget.
I know the Newegg link isn't any help to you, but hopefully it gives you an idea of what it will cost.
Now, if you're going to overclock you're going to need a better cooler. When you have the money, I recommend the Cooler Master Hyper 212 Evo. It's one of the best coolers for the money.