While you're getting a tumbler...
Grasskater--While waiting for yr tumbler, here's what you do w/the brass:
Inside: Forget it. There's nothing in there you need to clean. Any loose powder residue will drop out on its own, while you're handling the cases, but there won't be much there. Even tumbling medium in a tumbler won't clean up the inside of the cases much, except for cases that are "wide open" in design, like .45ACP. Even those won't shine up inside, although they clean out pretty good in the tumbler. Everything else I reload just stays gray to black inside, and never a problem.
Outside: If the cases are actually muddy, or covered with burnt residue, or such, I used to wipe 'em off with a dry cloth. Then lube 'em, size 'em, and remove the sizing lube with an alcohol-soaked cloth. Water works for most sizing lube, but the alcohol evaporates quicker, leaving the cases clean and dry. Cases that don't come clean right away (firmly stuck-on corrosion, or what-have-you) I toss into the scrap bucket.
In "common" cartridges, cases that are "problem dirty" aren't worth wasting time on. And scrap brass fetches > $1.60/lb. If you are reloading custom-made wildcat brass it would be different.
I emphasize, that this putzy hand-cleaning of cases is only for until your tumbler comes in the UPS truck.