That's great!!!! Congrats!!!
The wire in the kit is 32 gauge A-1 Kanthal.
You can find a roll of 200' for 11 bucks and under on eBay, Also try the 30 gauge when you find it. It's a bit thicker and easier to wrap.
Another FEEDBACK on your pics concerns the wire under the fillscrew. Don't forget to trim/cut it off so it doesn't short anything out. There shouldn't be any "left over" wire, when you're satisfied with your wrap. (except a little at the top for minor adjustments/recoiling, like Rick does).
Pretty soon you'll be doing all this in under 5 minutes! Buy a roll of it, an extra genesis, (hopefully a DID), and practice practice practice til it's old hat. The wick should last a few months, and the coil too.
There are all kinds of threads and videos out there on the Genesis style attys. Cleaning, dual coils, dbl wicks, u-wicks, ... all the advanced stuff that will keep you busy for a good long while. It's an exciting world!!! And we are one step ahead of the stupid politicians with their ever changing laws. . Congrats!!!