Suggestions on a CPU cooler for my FX 6300?

Hey,

I recently build a new budget gaming PC with the FX6300, an R7 265 and some other stuff that makes it work good, but the cooler that came with the CPU is absolutely terrible. In games like Battlefield 3 and Farcry 3 the cooler gets really loud and reaches over 4000 RPM according to Open Hardware Monitor, whilst my GPU is about half that at full load. So I'm planning to get a new CPU cooler, perhaps one that would be able to handle a small overclock, but nothing serious because my mobo would probably burn my house down or something.

I'm looking to spend less than £20, and I found the Cooler Master Hyper TX3 Evo on Amazon for £16.99. Is that cooler any good, or do you have any better suggestions? Liquid CPU coolers look nice, but they're pretty expensive, and I doubt it would be worth the extra seeing as I'm not going to be overclocking much.

Update
My case is the Corsair Spec 01 (I have a Corsair AF120 for exhaust) and my ram is Kingston HyperX Beast.