I've been tinkering with them a couple of years and I would recommend you pick up some pocket watch movements on Ebay and start there. As Marshall says, they are bigger and easier to learn on than wrist-watch movements. I have found that to be very true. Once you've gotten the basics down you can move on to smaller movements.
Try to pick up some running movements so you can at least get some experience tearing down and reassembly without having to fix it. Again, once you have the basics you can progress to repairing.
As far as tools, most of the common hand tools you can pick up from China (Aliexpress, DHGate etc.) for very cheap, but don't cheap out on screwdrivers or specialty tools. I picked up a used staking set for $250 and am now looking for a crystal install press. You may want to get an ultrasonic cleaner as well. Most movements I have purchased have been extremely dirt and never serviced.
Buy books, watch YouTube and you should be well on your way.