To wrap coil wire, I've used drill bits and even the ink cartridge from a ball-point pen (Zebra metal ink cartridges work great, lol)... as long as it is round and the proper diameter, and you can slide the coil off after you wrap it, you're good to go...
As for wire... it is BEST to use proper coil wire, designed specifically for making vaping coils... Kanthal, Ni200, Titanium, or one of the variants of Stainless Steel (SS316L is my preference). I would be cautious of using make-shift wire from a craft or hobby store because you have no idea exactly what is in it or how it would react to heating... or what type of toxins would be released as you heat it....