I recommend starting out with a watch repair book. There are several that can get you started.....
"Watch Repair as a Hobby" by D.W. Fletcher, and the old stand by "The Watch Repairer's Manual" by Henry Fried are very good.
Do a search on Amazon for "watch repair" and a number of good books are listed.
A good start is to pick up an old 18 size low jewel pocket movement to learn on.
This is how you start in watchmaker's school, with an old Elgin or other American made 7 jewel 18 size pocket movement that you take apart and reassemble.
You don't have to buy a lot of really expensive tools to start, just get a good Swiss made screwdriver set, some #3 non-magnetic tweezers, a good loupe, a hand puller, etc.
Add tools as needed.
When/if you buy a staking set, buy a good used K&D/Marshall/Mosley type on eBay.
K&D made these for other sellers under various names but the type of tool was the same. Other brands are often junky.
You'll need a bench or table top you can set on a bench to raise the work to eye level with no straining, and buy a GOOD powerful bench light.
Cover the top of the work area with either white poster board or a piece of light green or blue synthetic.
Buy a small ultrasonic cleaner, and some glass oiler pipettes. Buy some synthetic watch oil. Buy small cans of watch cleaner and rinse.