I use two tumblers. One is set up with Lyman nut media, orange looking stuff with rouge added. I run it in there for 1/2 to 1 hour to get the cases really clean.
The second tumbler has ground corn cob to remove any of the rouge, another 1/2 to 1 hour. This step keeps the rouge out of the dies.
Then I size and perform all of my other brass prep steps.
One more trip through the corn cob, 1/2 hour, to remove the sizing lube. Poke the cob out of the flash holes and load em up.
It may seem like a bunch of work but it has taken me many years and 100,000 plus case cleanings to evolve to this procedure. It may not be the best way but it works great for me.
I like my cases sparkling. They might not shoot any better than just good clean cases. If I feel they shoot better being pretty then I will shoot them better.
Also, get a rotary media seperator. it really speeds up the process.
Good luck.
Joe