Depends on what you mean by "watch repair". The set of tools you need varies by what you're looking to do. Most cheap "watch repair" kits focus on tools for replacing and sizing straps, swapping whole movements and modules in and out of cases, and changing batteries. The TimeZoneWatchSchool toolkits mentioned by Ron are higher grade tools designed for the actual disassembly, oiling and reassembly of mechanical movements. Repairing quartz movements is more of an electrical thing, and there specialized tools for that. Finallly, there's case work; buffing, grinding, hammering, soldering etc.
If you just want to rip apart some old, cheap movments that you don't care too much about, you can get by with some modeling tweezers, a set of dollar store screwdrivers and a metal file (becuase the dollar store screwdrivers won't have heads fine enough, so you'll need to file 'em down!). You'll likely gouge the bejezzus out of it though. And don't expect the watch to work when you're done (but props to you if it does!)
But if you're seriously interested in the watch repair, save yourself a lot of grief and frustration, and buy a <GOOD> set of screwdrivers and a couple of non-magnetic tweezers to start, and practice using them on some insignificant movements. EBay is chock full of cheap 7 jewel pocket watch movments that are perfect to start with; a nice 6s or smaller pocket watch is big enough that you won't go crazy, but small enough to still be a challenge.
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