Well cheaper or inexpensive are not words generally associated with reloading ,any longer that is .
The quickest least expensive method for ME ,as I had the ultrasonic prior to using it for case cleaning . Polishing is altogether a different animal .
Wet produces quicker and in MY opinion better results , shinier jewelry bling perhaps not . As with any surface for a flawless Piano mirror finish ,abrasions must be stepped out of the cases surface . Not unlike sanding or abrading in preparation for that $40K custom paint job , step abrasion removes previous abrasions 120, 150,180,220,280,320,400,600, 800,1200 - 2200 and finally polishing compound .
I just put MY cases that have previously been prepped and fired into the WET Tumbler with MY own cleaning concoction and works well enough for ME . Not to shabby considering these have #27 reloads on them ,1953 LC brass and still very much serviceable and YES that's what they looked like before I cleaned them up . Initially using the ultrasonic ,then simply tumbling for 20-40 minutes there after .
The necks and shoulders have had #8 annealing's ,last one this AM . As you can see the tumbler nearly erases any witness marks from a 1200 Deg.F. anneal temp . I figure it this way ,life's too short to spend an inordinate amount of time cleaning ,so anything that speeds up the reloading process is Good by ME. I prefer trigger time and load development over prep time . I simply mimic Lapua's annealing depth which is 0.5910" . So far so good ,cases are holding up to gas guns ,NO ripped rims separations or split necks .