I put my decapped brass into my small size Harbor Freight cement mixer and put in hot water and liquid soap (Ajax, Dawn, etc.) and tumble for 30 minutes to get any dirt out. Then I tip the mixer bowl to get the dirty water out and add fresh water to rinse the brass clean. Re-rinse until the drained water looks clear.
Next, the brass goes into a very large glass (Pyrodex?) baking dish and the brass is covered with a 3% solution of citric acid (I got this idea from the NRA book on Handloading). This gets the crud & carbon out and leaves the brass clean with a dull finish. You can stop here and use the brass for reloading after it fully dries.
However, in the matter of brass cases I am obsessive/compulsive so nothing less than a brilliant shine will do. So, it’s back into the cement mixer and this time it’s corn cob media treated with Nu-Finish for 3 hours. YMMV.
BTW, I bought my corn cob media from Graingers -- very nice people, very good prices.