You will find that everyone has their own method, and use every possible medium.
Alot depends on how much time and effort you want to put into cleaning your brass, how much brass you have to clean, and what you want it to look like afterwards.
Having been lazy at times, my pistol brass somtimes looked pretty bad. It was "clean", just not shiny and bright. But it all still fired fine, and was still accurate.
I've tumble my brass, a few hundred at a time (I put about as many as I could fit into the tumbler at a time while still leaving room for my corn cob, or walnut shells or whatever). Sometimes I add some polish and a cap full of mineral spirits, sometimes I go two or three tumblers full before adding more. I've used "gun supplies" medium, local store-bought tumbler medium, and I'm current using some farm-supply bought bedding (crushed shells).
I usually let them tumble for an hour or so, more if I have the time. Tumbling too much longer usually doesn't make that much of a difference in their looks.
I sometime "pre-wash" them if they are especially dirty, or if they've been rolling around the dirt/mud at a match. You need to dry them (same goes if you use a liguid cleaner) or they will tarnish. I've used the oven (on warm or low) or outside on a towel in the sun.
No matter how the brass looks when I start, they always come out looking better. Sometime very bright, sometimes not so bright. I save my "prettier" ones for matches (just so I don't take too much ribbing) but they all still function fine.
I don't think there is a "right" method. And the easiest methods may not satisfy your tastes. Try a few different methods or ingredients and see what works best for you.
As long as your cases are clean (not necessarily bright) they shouldn't hurt your reloader's dies or guns' chambers. Anything more is pretty much cosmetics.
ideas. 
