What kind of attys will you be rebuilding.
rba's or Rebuildable Drip attomizers. The basics. are wick (cotton, silica, ekowool, ss mesh). Wire or ribbon wire maybe in as few sizes. I have .4 ribbon wire which i do not use often. I have kanthal a1 32, 34, 36 wire. Some use 30 and 28 gauge. Mesh you can get from like 350 to 500 mesh. If you do mesh you will need a torch or torch lighter.
Tools :
Essential:
something round to wrap
coils in varying sizes and one some don't tell you about is a thin wire like maybe a small paper clip or the wire used in cheese cutters.
strong scissors
Small wire cutters preferably the flush cut kind. On this the outer side will be flat and the inside will be ground.
Small slot and cross point screwdrivers a perhaps allen wrenches which can also but used to wrap.
Other tools you may need:
Third hand type tool
Needle nose pliers
clips to hold wick and or wire like an small alligator clip.
An ohm meter should not be optional but some don't use them. (can save a lot of grief)
ruler.
A magnifier if you have eyes like mine. LOL
If you don't go below 2 ohms or even 1.5 ohms you will not likely need any wire bigger than 32 gauge. The smaller the number the biger the wire.
lastly lots of practice.
I'm sure i am forgetting something. Oh if you rebuild heads like protank heads or atty's like the Ithaca either special made wire that is whats called NR-R-NR NR means no resistance ( but really it's low resistance. R is resistance wire like kanthal. You end up with a wick that has a middle with Kanthal and long ends made of silver wire.
You can buy these premade or make or buy a welder.