For cases that have used smokeless powder I firstly clean my cases in my dry Thumlers Tumblers using walnut media (bought by the 1/2cwt from sand blasting suppliers, used to get 1 cwt bags but they seem to have got rid of those for most nowadays.
) with a squirt of car polish. I do this because I don't want dirty cases near my press or dies. After tumbling I then deprime and FL or Neck size followed by cleaning the primer pockets using primer pocket cleaning brush on my motorised Lyman trimmer, to me it would be worth getting the trimmer for its primer pocket cleaning feature alone.
You could deprime first and then clean as many here seem to do however I don't as I like to keep my tumbling medium as free from primer dust as possible. I would never put an uncleaned case anywhere near a sizing die, one scratch on the inside of the die and its ruined I also want as little debris as possible finding its way between my ram and the press.
For cases that have used BP I wet tumble in my wet Thumlers Tumbler using ceramic media. I find wet tumbling a real chew on but it is the only way to get the insides of the cases clean with BP. These cases are deprimed on the range immediately after being fired and dropped into a plastic bottle of water with some washing up liquid in it. The primer pockets come out clean witrh this process.
I have tried stainless steel pins and forund them to be no better than ceramic media and more of a chew on to separate from the cases afterwards than the ceramic even when I used a magnet.
Dry tumbling with walnut is my preferred choice for smokeless cartridges as it gets the cases as clean, not as shiny, as stainless but without the chew on a using a wet method and the extra stages of drying. Stainless will clean your primer pockets but I've also had issues with it sticking in the flash holes.
I remove sizing lube witha cloth immediately after the case comes out of the die.
