There are "battery changing kits" but in my estimation, (I have probably changed 10,000 batteries or more) you can do better buying separately what you need. You will get better quality that way also. If you are just doing your own batteries I suggest a good case back knife and a tool to remove screwbacks. Before you take off that back, however, use a brush, horsehair is traditional, to clean off the back so you don't introduce dirt to the inside. This is very important.
Get a battery tester. Always test the battery when you remove it. Don't assume it is bad. If you do you will get confused when you install a new battery and it doesn't work. Consider a demagnetizer of some kind. The kind with a button that sends a pulse. Often a quartz movement will start if you can force the train to move momentarily. Gaskets, buy a variety or discover a source for individual ones. A grease cup and some silicon grease for the gaskets. A fine point felt tip pen to write the date of install on the inside of the caseback. You need a press to reinstall the casebacks, lots of variety there. Don't overlook vintage tools. They are often better quality and cheaper. There are other tools but for a personal toolkit I don't think they are necessary. It may be that paying a pro is cheaper depending on how many watches you own. Plus, the pro has one thing you won't find in a kit, experience.