Hi inventor.

The wire should be fine as long as it is copper and has a coating. Magnet wire comes in many different colours of coating but they all do the same thing. If you are ok with ebay theres a good source on their who can supply all awg ratings at pretty much any size/length. His handle is "sword and treasure", do a search for magnet wire and he'll pop up.

The neon you are after should be similar to this one. Wiltronics Research Pty Ltd

I would recommend building the monopole sg and studying it before moving onto more advanced models. The triac can be a number of variations, or replaced with scrs or even npns.