I have a Lyman 1200 and a Lyman 2500. Use them all the time when parts need to be polished - walnut shell in the big tumbler and corn cob media in the other. I put a good squirt of liquid Autosol in with the media, I find it is just as good, if not better than Flitz - but far cheaper.
One thing to remember though, tumblers are not cleaners they are polishers. A rust encrusted part will not come out of a tumbler gleaming.

Thats the important bit - Tumbling is for polishing, not cleaning. You need to clean all the parts before putting them into a Tumbler. Otherwise all the dirt makes the media dirty and the polishing results are poor.