I started polishing cases about 50 years ago with just some 0000 steel wool. 15 years ago went to viberator with walnut shell and polishing compound. A couple years ago in Cabela's Bargain Cave and came out with a Lyman Ultrasonic, and Lyman compound. Also bought a large and small RCBS de-prime only dies, Love these, So I can clean cases before running through the resizing dies. On cases with several reloads, A 24 hour soak starting in 160 degree water and Blue high test Dawn makes the cases clean a lot faster in the ultrasonic. For pretty cases I like to clean in the ultrasonic. Then resize, do all prep work, wipe of as much lube as possible the put them in the Viberator with walnut shell and compound for that pretty shiny outside. Wear a T-shirt glove on left hand to keep them pretty. Here is a stand for drying wet bath cases. 16d finishing nails. The nails do rust a little. Now to a welding shop for some stainless steel welding rod and cut the into 3 5/8 inch lengths.
Lee zip trim and green scotch pad. Only takes a few seconds per case.
Then the occational vibratory with corncob.
Never used stainless, but i havent found anything that is better for cleaning the INSIDE of the case and primer pockets than the ultrasonic cleaners. It does a pretty good job on the outsides of the cases as well, but obviously not as well as the abrasive methods. I just simply use the steel wool approach to clean off any residue that is left. Dont really care if i impress anyone with shiny brass