Here's another "I do it this way" post.
First, I reloaded for 12 years before I got a tumbler. I wiped each case with a solvent dampened rag as I inspected it, never any problems with scratched/worn dies or chambers. So don't think tumbling has all the importance assigned to it today, and it seems to be one of the most talked about but least important subject on forums...
After a few years of experimenting with different kinds of media (I'm a "I wanna see for myself" kinda guy). including walnut, pet litters, glass beads, beach sand, wood chunks, charcoal, beans/rice/peas, and probably a half dozen more. I settled on corn cob blast media 14-20. Blast media is designed for metal polishing/cleaning and pet litter is for rats and lizards to pee on.
I normally tumble pre sizing as the step after tumbling is an inspection. Cleaning primer pockets has never been a priority for 99% of my handloading (handgun). I have two additives that I use sometimes; auto wax to leave a smooth light coating of wax to retard tarnish, and for hard cleaning I add about 10-20% hard resin pyramids, 3/8". If I want shiny brass In just leave the tumbler running longer...