if you want to go cheap stick with something like this
set the cpu voltage to fixed and set it to 1.1 or 1.15 and crank the multiplier up to 41 or 42 ( will show 4.2Ghz in the bios) and try her out
I had my 3770k at 1.4 and 5Ghz using a basic AIO cooler where the one I linked you my wife uses it on a 3970x overclocked to 4.6ghz with turbo turned off.
PS always turn off turbo
3570k is a great CPU….I am using one in my desktop. I have mine undervolted and slight overclock. Running 4.1ghz (1.09v under load if I remember correctly). I use a 120mm fan tower heatsink...this one if you want to know:
Got it for $10 on a great sale once. Any descent cooler of that size would be fine for you (typically on sale $25-35+tax). The most commonly recommended is the cooler master 212 (various models are available).
I leave all the power saving features on, turn turbo off, set multiplier to 41. Then I slowly reduced voltage offset until I got to the min that was stable. This way voltage will drop when under a light load (mine drops to 0.9v), whereas setting the voltage will have it at a fixed value on most motherboards (but it is easier to do).