Thanks for the great reply! I understand that there are a lot of variables in play. There's the strength of the magnet, the thickness of the wire, the coating of the wire, and the method of winding among other things. All of those parameters will affect the capacitance, inductance, and impedance which ultimately decide the output. Unfortunately, I don't think we have an equation for "warmth" or "twang".
Winding a coil is no small task. I understand that there can be up to 10000 windings and if it is done by hand then it's easy to lose count. The wire should be under some tension and the method of winding can have a huge effect on the sound. Scatter winding could produce longer windings than ordered windings of the same number (hence the greater capacitance). There would also be different turn-to-turn interactions of the magnetic field interactions. Thicker insulation would space the wire further apart from the neighboring winding and result in slightly longer lengths of total wire used and it would also affect the turn-to-turn interactions. A 0.001" thickness difference may not be much but with 10000 windings it will add up pretty quick!
Personally, I would be winding two humbuckers for my guitar kit (if I am assembling the guitar then I might as well assemble the pickups too). I would like my neck pickup to be soft and warm. It should almost sound like a mellow whistle, especially when distorted. So I imagine there would be a lot of higher frequency attenuation with emphasis on the lower/mid frequencies. The bridge should be brighter but not "twangy" or like a single coil in a Strat. If I want my guitar to sound like someone shaking a ring of keys then I will shake my own keys.
I was curious to see if any amateurs have successfully wound a coil and were satisfied with the result. Were there any "oooops!" moments during the process? Is there a recommended kit? I certainly don't want to buy a pickup to take apart only to rewind. At that point, I might as well just buy the premade pickup.
-- Boris