The end point for all of this expense, trouble and labor is to get a rock surface to shine. Depending on the level of silica or metamorphosed carbonate in the stone, a rock's surface can be smoothed so that it reflect light. To do this the grain sizes on the surface must be very small. Any irregularity will bounce or absorb light in a different direction and look dull.
Many rocks don't polish very well and the only way you discover this is by attempting to polish them. Some rocks will still have a pleasing look even if you can't get a mirror shine. Some less hard picture stones, banded rhyolites, and granites can still look good even if they have a flat appearance.
The worst thing for any finished rock surface is to have scratches, however. I would rather have a matte surface than a mirror with scratches. It seems the eye trains on that imperfection sourly. To avoid scratches the surface has to be progressively ground so that each stage is thorough. There is no worse disappointment than to get polishing a rock only to discover that you didn't grind the 200 stage thoroughly! There are two ways to check your grinding progress. One is the wet method where you grind the rock and then observe it carefully after each grit. In the light all the lines of the grinder should be parallel and of the same depth. The second method is to dry the rock thoroughly and look at it under the light at different angles. The first method is faster!
The traditional way to polish a rock after the 600 grind is to use a leather buffing pad and cerium oxide. My old friend gave me some mix of Cerium Oxide and a secret ingredient. That seemed to work very well. Later I discovered that it was a mix of Cerium oxide and Linde A*. You paint this on a wet leather wheel and then hand polish your stone. The wet sludge of the cerium oxide gets into any cracks or vugs in your stone so it requires washing and scrubbing thereafter. *This is expensive!
If I am not using the final lap in the Vibralap process (RP 61 on felt for 6 hours) then I have shifted to using buffing pads on the bench motor. This motor runs slower than a typical grinder. The pads are soft cotton and need to be separated for each compound used. I have one for each of the polishes I use (Tripoli, White Diamond, Red Rouge, and Blue Diamond).
One advantage of using this system is that it is dry. Rocks do not get filled with polish much and if they do it can be blown or brushed out. Usually it is gone by the time I am finished with the last buffing pad.
For rocks polishing after the 600 grit stage I use Diamond, red rouge, and blue diamond. The black and Tripoli rouges I use for metals and woods and sometimes a stubborn scratches on a rock. The white diamond will polish the rock and leave some cloudly areas and the blue will remove those. I have been doing this for a while now and am very pleased with the speed of the polishing and the results.
When the rock is finished I buff it with a wax coating just to preserve the shine. It seems to help those rocks that are a bit on the matte side of the spectrum as well.