You could start by sort of reverse engineering movements (disassemble and reassemble).
Start to build your own tooling.
Then make a copy of the bridges and baseplate.
Try to change the geometry of the bridges and baseplate, keeping the same moving parts.
Then build your own moving parts.
Start from massive clocks to "table clocks" to marine clocks to wristwatches movements.
And it could be very expensive, wood clocks are cheaper, less time consuming. There is great stuff and ideas online.
For example, see the timer from Ugears there is mind-blowing tricks hidden in this model.
It's not possible to buy gears due to the "module" (I don't know how to translate it), it's a factor of scale that influence the spacing between gears.
The hardest parts are the springs (balance spring and mainspring) and the screws (there are so small, it's a specific norm, see NIHS for Normes de l'Industrie Horlogère Suisse).
For the gear cutting, there is an example here [pdf link]: http://www.cowells.com/docs/cutter.pdf
There is a lot of custom machine tools, many of them are needed to resolve problems that an individual doesn't care.
But there is always alternative ways and it's the fun and watchmaker's task to find them!
So there is not really indispensable tools as it depends a lot of the project. Expect if you want to make specific watch decorations, like perlage, guillochage, soleillage...
I can't find links but there is an operation named roulage where the guiding parts of the pinions are hardened, it's not indispensable if you don't want an industrial grade, kind of.
This is more clock making rather than watch making, but check out the clickspring channel on youtube. He builds a mantel sized clock from scratch in his home machine shop. Amazing stuff and beautifully done videos.
You could start by sort of reverse engineering movements (disassemble and reassemble).
Start to build your own tooling.
Then make a copy of the bridges and baseplate.
Try to change the geometry of the bridges and baseplate, keeping the same moving parts.
Then build your own moving parts.
Start from massive clocks to "table clocks" to marine clocks to wristwatches movements.
And it could be very expensive, wood clocks are cheaper, less time consuming. There is great stuff and ideas online. For example, see the timer from Ugears there is mind-blowing tricks hidden in this model.