I use a Lyman tumbler or vibratory cleaner, whatever... with the bottom that is supposed to pour out as it's vibrating. I don't use that option as it takes too long and there's still tonnes of media left in the cases. I bought the assessory made by Cabela's so you can just pour the media out of the tumber basin, and twist the handle to get all of the media out of the cases. This setup works well for me.
I have tried the Lyman brass polishing solution and other similar products. I won't use them again. I don't see the point of spending the extra $5-$10 here and there and the time involved to make brass cleaner or shiney'er to "save my dies" when I can buy a new set of carbide pistol dies for $30 "if" the day ever came where I thought my sizing die was too badly damaged.
I tumble all of my brass before sizing to clean the crud off, and after to clean the lube (with bottle neck cartridges). Use a carbide die for your 9mm, you won't need to worry about the lubing process.
I did the soapy water in a coffee can method when I started out, but I found the biggest pain in the ass was waiting for them to dry. You almost have to position them all with the case mouth down on a tray because the water pools in them. I didn't like this method.
I thought I read somewhere about people putting the brass in a bag with some sort of media (rice maybe?) and putting it in the dryer or something like that. Maybe that's a bad idea, I never tried it.
I think wiping the brass off will be sufficient for now, lets face it you won't be putting thousands of 9mm rounds down the barrel here doing this method. If you plan on getting into the reloading game, and it sounds like you are - you will be purchasing a tumbler at some point so if I were you I would just do it now and save myself the hassel.
Good luck with your 9mm loads!