For firearms I use hoppes 9 or elite, depending on the finish, for the cleaning solution. I'll let them soak while I pop primers and throw the shells in the tumbler. As others mentioned, the cylinder face doesn't have to be spotless though I will do mine every couple years or so. To do them I just use Mothers mag or billet polish and a soft cotton rag. Takes about ten minutes or so to get it all. Here are some of the stainless ones:
I also use Mothers polish on exteriors that have a high gloss finish like my Vaqueros. I puts a really deep luster on them.