I tumble after depriming, then use the RCBS media separator to remove the media. I also check every flashhole and pick out stuck media with a toothpick. The kaytee bird litter I use (along with some optional lyman brass cleaning solution) seems to leave the brass a little dusty, so I rinse with water in a strainer setup (only for the brass!) that I bought at the dollar store and lay out to dry on a towel for two days. I'm a patient sort of fellow.
If I FL resize I use lee lube (water soluble) so to remove it I just do the rinse cycle with some hot soapy water, then hot water, lay out to dry again.