Probably you will want to differentiate between "clean" and "shiny". When I started, I would place a pile of fired brass on a bath towel (for that purpose) - then slosh on some white gas - camp stove fuel. Lift ends of towel to make like a hammock and slosh back and forth - that would remove grit, grunge, etc. from the cases. Then they are "clean" - but not shiny. Rolled them on lube pad, re-sized, which popped out the primer. In those days, I used to then clean each primer pocket with an RCBS (?) round brush tool. After cleaning out the pocket, I would trim to length and chamfer the case mouths, and de-lube - often using that white gas and towel, since the lube that I used was an oil based stuff, back then. I would then re-seat a primer using the arm on the press - then dispense powder - for "critical" loads that was weighed on beam scale and trickled to weight. For less critical - that was throw by volume from powder tool, and check about every 10th for weight. Seat bullets. Fire and repeat.
Now-a-days, I tend towards wanting "shiny" - for no real good reason, over "clean" - I doubt it makes me shoot any better. So I de-cap, usually in a de-capping die or with a Lee punch. Then into a rotary tumbler thing with stainless pins, Dawn dishwashing soap, Lemi-shine powder and room temp water - makes the brass "shiny" inside and outside of the case and more or less cleans out the primer pocket. Lube and resize - I trim to length, chamfer the case mouths and wipe off lube while spinning them one by one in a Lee case spinner stud (current lube used is water based - wipes of easy with damp rag). I now dispense powder with an RCBS ChargeMaster Lite, although the Hornady beam scale and trickler are set up and ready to go. Seat bullets. Fire and repeat.
EDIT: - I re-read your initial post - you are loading 9mm, I presume for a handgun - I have no experience at that - so can likely ignore most of the specifics of how I re-load - was based on many 308 Win and 243 Win cases for rifles.