The compound you use is determined by what your final desired finish is, as well as the amount of prep work you did prior to buffing.
Optimally you do as much hand prep work as possible, so that the actual buffing is very light and quick.
It is
possible to go from a rough ground finish (like 80-120X) straight to buffing wheels w/ coarse compounds (all compounds are different, but a black or dark gray- fast cut compound is usually really abrasive ~120-240 grit) and work up to a mirror polish.
However, that is not going to give a pristine finish with crisp transitions. It's going to wash out any crisp/sharp transitions, and give you a smeared, wavy surface. Maybe not on a big round object made of soft material--- like a teapot or something, but definitely on a knife blade.
If you want an absolutely pristine mirror finish on a knife blade, and want to retain crisp transitions--- One method that I know for a fact works well, is to hand sand (each progression in grit should be at an opposing angle to the prior grit) up to a very clean 2000X finish. Then lightly buff with a spiral sewn wheel loaded with Green Chrome compound. Then clean all the residue off your blade (don't want cross contamination of compounds). WD-40 works extremely well for this. Then go to a spiral sewn or loose wheel, loaded with Pink No-Scratch compound.
The green will give you a mirror, but typically leaves a bit of a haze. The pink no scratch compound follows up removing the haze or smoke look and gives you a full mirror.
I only do this on certain elements of my knives for contrast in color and overall effect, but I did it on blades for quite some time early on.
Hope that helps.
