all you need is wire some thin drill bits for mandrills to wrap your wire around, cross head screwdriver shafts work too ideally something 2mm, 2.5mm, or 3mm in diameter to start with probably.. next some clippers to snip the wire, electronics side cutters at £2-3 a pair are the top shelf option nail clippers work in a pinch.
Then you want a nice sharp pair of cotton snipping scissors and thats about it.
so
1) wire, 2) mandrills (drill bits/screwdriver shafts..) 3) side cutters, and 4) scissors..
edit .. and 5) cotton/wick.. i use muji pads a Big bag (2 years worth at least for about a fiver..)
a tenner should give you plenty of change for a coupe of spools of wire,, (0.4mm K-A1 is probably a good robust witre capable of a m=nice 7-9x wrap coil on a 2.5-3mm mandril for circa 0.5ohm..)
thinner wire is less robust, Nickel is soft like butter and a pita and SS is much more springy..
so if looking for a tc vape go for SS316 wire imho..
To fully kit out extras which are nice but nor needed are an ohm meter (99% of regulated mods will read coil ohms for you..) atty stands make like easier standing an atty upright..
Ceramic tweezers with a grippy loop handle are great for the grippy loop when you need to open a stubourn atty
and a nice set of jewelers/electronics screwdrivers and allen/hex keys for when you mislay the specific tool for the atty your building now..
so you can equip yourself for less than a tenner and can fully equip witj all toys for less than £20 imho
DO NOT BUY A DIY COIL KIT - Shit scissors, mini screwdrivers,, not ideal and quite costly compared to a 15 minute ebay/amazon shop..
btw if you dont get on with diy coils just but premade coils in lots of 50x etc from china for a $ or 2