stuff said here is valid. for "punch" you want compressor/exciter action to bring up the transients. For heavier sound, compressing to even out tails will make sound more massive.
What you exactly do depends a lot on the sound you're after. Many ways to rome.
For a dirtier sound try using a distortion in shape mode with drive around 1/3rd of range, and full dry, wet carefully dialed in not more than 1/4th.
With low end multiband compression, you can also put a gate on the low end to eleminate rumble where it is not wanted. Will make further steps sound much cleaner.
Then the drumfunk people seem fond of emulating a 12 bit sampler somehow which will generate a very aggressive high end, and the lofimat device with freq around max can yield very similar sounds.
Eqing can be used to clean up the break and do what the original engineers couldn't do. Like if you find some ringing/resonant tones in the break, you can cut it out with a very narrow notch, and get a much cleaner break as result. Many of the classic breaks have those resonances, the amen for example I cut several notches out of the midrange. It takes some experience and good ears and eyes watching the spec analyser, and confidence in sweeping and finding them with an eq. Especially the midrange benefits a lot if you kill the right resonances. a/bing the results is an interesting experience, because you will suddenly hear all the muddy resonances that you struggled so hard to percieve before.