In my opinion, stick with a Tele. The bridge is easy to set up and intimate and the hardtail will give you more sustain. You can mix and try pickups to get the sound you want.
For the body and neck, some ideas
- Warmoth
- MJT, especially if you're looking for pre-finished / reliced.
- Bodies off Reverb / EBay in various states of loaded-ness, and necks similarly. From what I can tell, there's companies that buy blemished / showroom-damaged guitars and tear them down for parts. Often there's a tiny chip on these bodies that wouldn't bother me, and so you can get an American-made body, painted and loaded with pickups+electronics, for fairly cheap in some cases, if you can live with a dent or chip.
- Saylor guitars - they made me a great Telemaster semihollow a few years ago that I sanded and finished with tung oil. If you want a Telemaster shape, or want fancy woods, I'd contac Saylor before Warmoth.
I'd avoid the knock off $99-ish kits on EBay and Amazon imho. You don't have to use Fender-licensed parts, but those kits are the cheapest mass produced parts they can make. For a first build, my opinion would be to use some relatively nice but not extravagant stuff, primarily licensed by Fender or made by Fender. Just my opinion, though.