I like shiny brass. Many people will tell you it's not necessary, but technically neither is washing your car. It will still drive.
Three steps for me - deprime, wash, polish.
1. Deprime using the Harvey Deprimer. The dirtiest reloading step for me. Check cases as I go for damage. Hands need a *good* wash afterwards - don't eat or drink while doing this. I don't want that crap all over my turret press, in my lungs or my bloodstream.
2. Wash the cases with a Harbor Freight ultrasonic cleaner with a drop of Dawn and a dash of Lemi-shine. A little goes a long way. Usually run it for 2 cycles, and give them a few stirs during each cycle. Rinse them under hot water in a colander. Dry them out by rubbing in a towel. Some remnant water will remain in some cases, generally a gentle blow through the primer hole clears anything being held inside by surface tension. For me using the ultrasonic is a critical step I wouldn't skip - given how much crap comes out of the cases when depriming, I want that stuff out of the cases before putting them into a dusty tumbler process.
3. Polish the cases in a Harbor Freight vibratory tumbler with HF walnut media and a cap of Nu Finish, and some torn up USED dryer sheets if they're available. Run the tumbler for a few minutes to distribute the car polish BEFORE adding brass, otherwise you will get cases with clumped media inside of them. Run from anywhere from 2 to 8 hours depending on whether the cases are decent to start with, or range pickup. The garage is a good place to keep the tumbler because of noise. When done strain the media out through a colander (it's good to use over and over). Again give the cases a rubdown in a towel to remove any remaining dust, and check each primer pocket for stuck media. Biggest thing I've found to keep the dust down is to winnow the walnut media when new - basically take a bunch of the stuff outside on a breezy day, and pour it from bucket to bucket letting the breeze winnow the dust out. The difference this makes to dust on the cases after vibratory tumbling is amazing.
At this point they're as clean and shiny as I can make them. I usually deprime as part of my post-range cleanup, but will do the wash & polish step in batches when I have enough dirty brass to make it worth my while - do the ultrasonic in the evening, and tumble the next day. If I had a wet tumbler with SS pins, that would combine the wash and polish into a single step - but I already had the ultrasonic for cleaning parts, and it was a lot cheaper for me to just add on the vibratory tumbler and media than the wet tumbler and pins.