Wire Temco Electrical. Cheap, free shipping, and the same wire as "expensive" vapr wire. Cotton, Japanese organic cotton pads roughly $10 for a pack of 80 from Amazon. Should last you a few years.
Tools. A good part of scissors for the cotton. A wire cutter or nail clipper for the wire, and a drill bit of known size like 3 mm to wrap on or a coil jig. Tweezers help.
You can also buy a build kit from someone like Coil master with all the nice stuff in it that will be more than enough including an ohm meter and build deck for $30-40. I recommend it but as you can see from the list above not a requirement.
I would agree that a kit is a nice thing to buy. You could dig around and get the stuff cheaper, and probably higher quality, if you built the kit yourself. But for starting out I'd recommend buying a kit because it can be confusing for a new person. The Coilmaster kits are pretty good for someone to start with. I bought the Coilmaster V3 for about $36 but I am seeing it for $40-$45 now. I don't regret getting the kit and in hindsight I'd do it again if I were just starting out. The cotton that they put in it is crap though. You'll want to buy some different gauges of wire and definitely some decent cotton to go with it.
As others have said watch some YouTube videos of people making coils. Try to find tutorials of people building on what you use so you'll know how to wick the coils efficiently too. It can be really frustrating at first, so don't give up. You get a real sense of accomplishment from doing it after using store bought atomizers.