Rocketrob, a Tele is a good choice for a first binding job I think. BTW, Stewmac has a very good binding tutorial on their site that's worth a read.
In addition to ensuring your binding channel is as square as possible, it's advisable to examine your binding strips on the edges to see if they are rough or not. Typically, binding strips are cut to width from wider stock and the edges may not be smooth. If they aren't, dragging them lightly across a file will help flatten them and ensure a good fit in the channel. I also "degloss" the flat side of the binding on the side to be glued by scraping lightly with an exacto or single edge razor blade. That helps to ensure good glue adherance. When using Weld On, be careful how much you apply as it will squeeze out and have to be cleaned up. Be prepared for that and clean it up quickly. I use the binding tape that Stewmac and others sell as I find it has the right adherance qualities. IMHO, green painters tape isn't tacky enough. I do use a heat gun (actually an old cheap and not very powerful hair dryer) to help bend binding. You do have to be careful this way not to go too fast, but a little practice with the binding in advance will give you a good idea how much heat to use. Be extra careful if the binding material is celluloid nitrate as it is flammable, although I have never come close to having a problem. I find a heat gun gives me more control in specific critical areas without having to heat the entire strip at once or worry about water.
In any case, have fun and share the results.