Everyone has their 'best' ideas and they are right. The problem is to find the way that works best for you and what you need to get done.
How much and what size?
I can get by with an old 'T' shirt and rubbing a dozen specialty cases with no problem. Move on to a K of .40s or .45s and that method isn't viable. 9MM would be more of a pain, in the hands.
So, how much of what becomes a major question.
I have but seldom use a 'rattle tub' with various type of grit/media. It makes dust, is noisy and cleans lots of brass at one time. From time to time I will obtain fair sized quantities of brass that is nasty, grass, gravel, twigs and dirt. The 'rattle tub' ends up being my first step.
I have a little sonic cleaner and I like it... for small jobs. It is my choice when cleaning a BCG from an AR but not for brass. Just too small of case numbers.
My, current, preferred cleaning method is a double rubber canister rock tumbler with Dawn detergent with water and stainless steal pins. Being a nut, I do a quick cleaning followed with sizing and de-priming and follow up with a full cleaning. Some powders will leave a shell on the inside of cases and sizing breaks this and the liquid after the second cleaning is just as black as the first time. Now to the concerns, not problems. Some times with some cases, I will get pins stuck inside of the brass (.223/5.56 type/sizes) and these require some shaking to get out. A few times two pins will wedge in the flash hole and need to be pushed out. And then there is the drying.... I picked up two 'food dehydrators' at yard sales. They dry brass quickly with no fuss.
So, your needs will be the determining factor. I can only tell how I deal with the task.
Load with care and enjoy.