In my reloading efforts so far, I have deprimed before wet-cleaning my brass. Most of the gross stuff is in the primer, so keeping them out of my wet cleaning kit (Just a 1qt mason jar) is a good idea.
I spurt in a little Hornady One Shot in the quart bag that I picked up the brass in, shake it around a bit, then size/deprime.
After I collect the spent primers, I dump them into the mason jar with hot water and citric acid and shake it around a ton until my arms get tired. Then, I re-fill the container with just water, shake some more, drain, and dry them overnight.
That has worked quite well for me so far.