I actually discovered pretty early on that my interest was more in clocks than watches, but the early explorations in the watch realm were almost entirely applicable to clock repair as well. I have since repaired at least a hundred clocks and pocket watches. Next month I'm going down to the NAWCC school of horology in Columbia, PA to take my third workshop there, this one on the repair of wooden works clocks. The school was closed for a number of years, but has fired back up in the past few and I know they're actively working on getting more watch repair workshops going. Last time I was there they were just putting together a killer watch lab with some very expensive benches and equipment.
You will need a set of flat headed screwdrivers. These are 80% of the tools you'll be using.
If you are approaching middle age, you'll need some magnification. I dont like loupes (those lenses you hold to the eye), and the visor mounted magnifiers are also not that good for me. I got a second hand long armed stereo 10x microscope for £30 which is perfect for me. You might just want a big old magnifying glass.
You might want a movement holder, again you can get super cheap ones, but second hand ones are better (because the shit ones are thrown away). they are basically specialized vices, or tiny little buckets(those are custom to each movement though.)
Next, start off with pocket watches, they are much bigger and more forgiving, and also cheaper.
In the uk: H samual, Thos russel are good brands to look for anything £20 or less.
For america: waltham/elgin (they often have broken balance though so watch out ) Eglins and Walthams look a lot more pretty, and have a better standard of finishing than the english counterparts.
There are 10x more pocket watches than owners interested. Theyre incredible machines... but their greatest use is practice materials for aspiring watch repair technicians.
They're expensive to repair because few people have the skills and tools. The demand is so low. (I have two)