First thing I'd suggest is to leave the hand held tools alone - contrary to popular belief, these are really not used when refinishing cases. In the refinishing training I've received from both Omega and Rolex, a hand held rotary tool was not ever used.
Get yourself a proper bench lathe (polishing set-up) that uses large buffs. 4 inch diameter are fine, but often larger buffs are used...this is the polishing room at JLC:
As you can see, these are very large wheels. Wheels of differing profiles are used for hard to get to areas:
Note the wheel at the very end of the spindle in the foreground.
For compounds, what are you planning on polishing? The white and red are basically for precious metals - that's not to say they won't work for steels though.
Personally the only Dialux I use is grey - this is a more aggressive compound for removing heavier scratches in hard materials, such as stainless. I generally use this with a hard felt buff that doesn't wrap around the surface I'm refinishing when pressure is applied - this is how you preserve sharp edges. It brings up a good shine, and then all that is needed is a colouring compound that applies that final lustre. For that I used an unstitched muslin buff, with Picasso Blue compound.
Some other things...
Keeps your buffs separated and organized. Don't mix compounds on a single buff, and keep the buffs clean. Let the compound do the work. Trying to remove too much to get every last bit of that deep ding or gouge out, is when you are most likely to ruin the shape of the case, so be conservative with how much you remove.
Use an air extractor or wear a mask - both if you feel it's needed.
You have nothing there to accomplish other surface finishes - nothing to apply a grained or brushed finish with...not sure if you are only polishing, but if not that has to be considered as well.
