Tumbler: https://www.amazon.com/dp/B001MYGLJC?ref_=cm_sw_r_apin_dp_7G9XF3PM80HJ1VJVM475
Tumbling medium: https://www.amazon.com/dp/B09KH3NZM5?ref_=cm_sw_r_apin_dp_4AVHK82VKNE4QQW2BRJZ
Polishing compound (mix in with the tumbling medium, just a couple tablespoons): https://www.amazon.com/dp/B00BQA3VEK?ref_=cm_sw_r_apin_dp_Q4A4HE1XR8G16JM91TRV
I only recently gotten into using a tumbler after for the last few years insisting I could do just as good by hand... yeah. It does take a while but it outs anything I do by hand to shame.
Items I use:
Tumbler: Pretty much what everyone uses. https://www.amazon.com/dp/B001MYGLJC/?coliid=I116WR7GYXWFQG
A small funnel that can fit over the central rod that is used to hold the lid down to avoid any scraping of it against the dice. The tumblers designed for metal items, so for dice it needs something to cover the center rod.
5 pounds worth of Non-Abrasive 3mm Porcelain Sphere Polishing Tumbling Media. There are a lot of brands out there (Mine is Craft.Box) but really find whatever is cheapest at the time. Most these brands source from the same place and just slap their logo on the container. Mine came in 2.5lbs batches and I needed 2 to fill the tumbler to let dice sink down into it. It sounds like a lot but it's not.
Polishing Compound: A little goes a long way, two squirts and let it go. It's recommended as it's also water based, so if it seems to 'dry out' in the tumbler a spoon of water and letting it tumble a bit is all you need. Also easy to clean as you will need to clean the medium and the tumbler every once in a while. https://www.amazon.com/dp/B00BQA3VEK/?coliid=IHQ9UHXAK9KRD
Fine mesh bag: For cleaning the medium super easy with out risk of losing any of the small balls. Just need dish soap and water and wash away. The amount of medium fits half of one of those bags so offers plenty of room to scrub. https://www.amazon.com/dp/B0737ZQ5L7
That it is really. Yes the tumbler will be a bit loud but it seems to be around that of a person talking. I have mine in my room and I can easily drown it out and with headphones on I don't really hear it. If it does bother you it can easily be sat in say a bathroom or closet.
Highly recommend when just starting put in the medium and let it run with a little bit of water to both clean the tumbler and the medium but also to be sure the tumbler is letting the medium both spin around the bowl, but also pull it to the center and down and around back to the edge.
Polishing time will depend on how sanded your dice are. Keep in mind, this POLISHES, it don't sand. You will still want to clean your dice up but let this do that final polishing. You CAN put in dice that are mat in finish, like if you used the first set of zonas on them.. but it could take days to get them to that glass like shine. Where as if you cleaned them up then out them in, could be 8 hours to 24 hours... or longer, again it depends on how clean the dice are and how shiny you want it to go.