I use a Hornady Ultrasonic cleaner, does a fantastic job cleaning inside and out, including the primer pockets.

Depending on how dirty the brass is, and how clean I want it to end up, I use different solutions.

If I want pure clean, bright shiny brass, I use 50/50 white vinegar and hot water with a shotglass of dish-soap or Hornady cleaning solution for 15-20min. Then hot water with a shotglass of hornady solution for 5min, 5min cycle rinse with distilled water, and they look bright.

It's pretty cheap per washing. I wanna say I get 250ish pieces of .223rem brass in each batch. Would fit more, but wouldn't clean as well. It DOES clean better the fewer pieces you install.

Here's a link for cleaning you might be interested in:

6mmbr.com Ultrasonic Cleaning Guide

My method is similar to the "Clean and Shiny" recipe from Baney about 2/3 down the page. I haven't seen any benefit of Birchwood Casey over the Hornady solution, and I got a sale deal on the Hornady solution 2 yrs ago, bought enough to last me about 3 lifetimes at the rate I use it.

If I notice excessive char in the primer pockets (something I've learned to gauge), I may pocket brush them before. Most of the time, the solution takes care of it, no matter how dirty it is. If the solution is really dirty, or if the primer pockets don't come clean, I may brush them during the cleaning process, or re-vinegar them or re-hornady solution them. Mostly that depends on how I feel that day. I don't really have a standard method because it doesn't happen very often.