Budget Watch Collecting/Learning to fix watches
The best way to learn to fix watches is obviously with a good teacher, however that can be difficult to find.
Gather a minimum toolset.
Gather mechanical movements. Bridged movements are best, but for educational purposes very low quality movements are fine. Avoid full plate or 3/4 plate movements as found in Timex, Westclox and similar inexpensive watches--These are extremely difficult to work with in a way that will teach skills needed for "normal" watches. A bigger movement is better, but a small bridged movement is preferable to a large full-plate. Women's movements are more plentiful, but harder to reassemble. They may be worth the attempt, just in learning to handle parts. Fewer complications (calendar, auto-wind) are better, and to some extent even badly damaged movements can be useful.
An old wind-up alarm clock can be useful in learning how a movement works--These usually beat a bit slower, and have larger parts that make it easier to visualize and follow what is happening. It can also be useful to study a working old 400-day/Anniversary clock, the type usually under a glass dome, with a slowly-rotating pendulum. Most of these have a visible escapement, and the slow rate allows you to see the different steps of the escapement.
Try to disassemble and reassemble a movement without breaking pivots or shooting parts across the room. Test the train before reinstalling the pallet, this will let you see if the train works properly
Next, try to clean and oil a movement.
Once you have successfully cleaned and oiled a movement, you may be ready to clean and oil the movement in a wearable watch.
Movement types in rough order of difficulty
Timex These are odd cases--A Timex is very difficult to completely tear down, however they were designed to be cleaned and lubricated with minimal disassembly. The official factory procedure has you remove the balance and some of the winding system, the rest is placed intact in the cleaner. In some cases, they will start running again just by swishing them around in lighter fluid.
Generic Swiss bridged time-only.
Seiko "magic lever" automatic--Without calendar is easier, but Seiko's calendar system is generally much easier than Swiss.
Swiss automatic--Variable, but generally more complex than Seiko.
Swiss Calendar--While some of these are reasonably simple, some were designed by a close relative of Rube Goldberg. I've frequently found a non-quickset date only to be more difficult than a Seiko with quickset day and date.
Chronograph. Many professional watchmakers refuse to work on these.