... from my jewelry / stone polishing experiences:
1 - the harder the material, the finer the abrasive to reach a high-shine ... and the more steps. Metal is softer than stone, marble is softer than granite.
2 - work in stages from coarse to fine -- probably wet-sand -- up to 600 grit (finer if it can be found)
*** (be sure that you clean between each stage so that no coarser abrasive is left from the previous stage)
3 - coarse polish with a cotton buff (some jewelers use tight-weave carpet) and tripoli
*** each polishing compound *MUST* be used with a clean buff -- mark the buff so that only that compound is used with it and keep it wrapped in plastic or some other way to keep it from becoming contaminated with a coarser compound ***
4 - follow the tripoli with finer grades of polishing compounds:
- white rouge next and then
- red rouge
using those steps: wet-sand through 600, buff with tripoli and then white and then red rouge works great on all stones I've ever polished (have never done diamond) and produces a mirror finish. I also need to do this with granite and have no idea how I'm going to practically carry this out (I no longer have my large buffer). Can 600 grit be purchased for a belt sander? All of this will obviously be easier if it is polished before it is installed.
The buffing supplies can be purchased at a jewelry supplier -- I don't have any experience with the vendor below, but just did a search and found this page, it has pictures of the polishing compounds and prices:
here is an example of and a source for buffs:
NOTE: It's been a long time since I made jewelry and the above is how I polished stones ... but there are probably better ways to do it:
... this company has flexible diamond pads to 3000 grit. This looks like the better way to go to me, as my method above would take a very long time (it works okay on a small stone). A complete set of pads from 50 to 3000 grit can be had for $150 and will fit on a grinder.