I have several gallons of solvent. When I have completed resizing, I put the cases into a mason jar (s), pour solvent over them, and shake the jar. This is for rifle cases, I use carbide cases for pistol brass.
I then take a large funnel, put a rag inside the funnel to stop the cases from going back into the can, and pour the solvent and cases into the rag. The rag catches the brass, and the solvent will go back into the can, minus a small amount of solvent.
I then will put the washed cases into a cardboard box large enough for the cases to lay flat in the box.
leave the box outside until the remaining solvent has evaporated. It will stink up the house, and is dangerous if it is flammable.
Do not use mineral spirits as a solvent.
When all the cases are dry, I throw them in my Lyman 2500 turbo cleaner, along with Lyman ground up "green" corncob.
After a little time, the cases are spotless, shiny, and look like new. I have a RCBS tumbler media separator which is excellent to separate the media from the cases.
I do have to check the primer pockets for small pieces stuck in the flash hole, but that is easy to remove with a small phillips screwdriver. Be sure that you do this, as a piece stuck in the flash hole can cause grief.
I read a very interesting article in I think the Handloader magazine about chemical residue building up in cases from polishing in a liquid media, sticking to the inside of the cases, and causing pressures to skyrocket. It was only with small cases like a 17 remington.