Vandy Vape Kylin
Vapor Tech Kanthal A1 Wire (24 gauge)
Wick 'N' Vape Cotton Bacon Prime
Coil Master Coiling Kit V4
Is this a good start?
I hear the Kylin Mini is really nice for flavor, and it's single coil, so you don't have to worry about getting 2 coils to glow the same way.
Wire sounds fine, 24Ga SS is the smallest gauge that holds shape really well when working with it, I assume A1 is similar.
Brand name cotton is a ripoff, but if you want to try rebuilding before comitting to a bag of imported organic japanese cotton, why not?
I use a simple rod/coil jig instead of a coiling kit, but I've heard good things about Coil Master kits.