There are many pro kits that jewelers use> But you can find ones on ebay that work just as well. There are basically 3 different type backs. Snap on, screw on, and twist on. Now within each there are also different styles and can require different tools. Even some of the better watches that have snap on backs you could never snap them on with your thumbs if you tried for days. They require exact pressure in the center of the back and can only be done with a tool. Some screw on backs have keyways in them to make it easier and these are usually higher end. Others have just a bunch of ridges and this requires a certain tool.
Batteries, there are hundred of watch batteries so order only what you need. A good watch may have the battery number written on the back. I have included a link that hope works but you can google utube videos and also list of tools. Good luck. You can save a few $$ if you do it by yourself but many times a reputable jeweler will do for free and just pay for battery.
https://www.mywatchvilla.com/how-to-remove-watch-back/#:~:text=There are three types of watch back casing,,2 Snap-off Watch Back 3 Watch-Back With Screws