My advice is this:
You get what you pay for.
Like you, I had this mad desire to go out and fine some obsure, cheap harmony-esque guitar and expect it to sing.
I ended up finding this really cool looking Teisco Jaguar Copy that at some point was repainted this strong yellow color. Got it cheap enough that I had free range to customize it and get it sounding nice.
Long and short is that the guitar was a dead end. Despite how cool it looked, no amount of realistic work could revive that thing. It sits, to this day, next to a few projects and other unloved guitars; out of sight and out of mind
That being said, another project where I had a ton of luck was with one of those harmony strat copies that you can get on ebay for under $100. The electronics were pretty solid and the neck pocket is similar enough to a fender's I popped on an aftermarket neck and it plays pretty well. Its a little beat up which gives it a nice look.
Aside from all that, I would still steer you away from trying to revive a clunker, because the chances are not in your favor.
Everybody above has given some solid advice. I can only supplement it with:
- Single Coil or P90s are going to give you the best tone towards using a Fuzz or getting a sound like TBK. Avoid humbuckers altogether, I'd say.
- Hollowbody or solid body would be fine. Both have perks and drawbacks compared against one another. Hollowbody will likely cost more.
- Tremolo or vibrato is necessary. I like slapping a Bigsby on my hollowbodies for the looks.
If you aren't against a big name brand, I'd recommend the following
Epiphone Casino - John Lennon Edition
- It says John Lennon (love or hate him, but you probably at least respect him) and all, but its nice guitar built to better standards than Epiphone's standard collection.
Fender Highway One Stratocaster
- Any Fender Stratocaster is a safe choice. I have a highway one tele and love it, but they have quite a few options. The american standard stratocasters have alot of perks as well.
Gibson Les Paul Junior
- Absolutely LOVE mine (TV yellow). Very great sound out of the box with the p90s. My current favorite at the moment.
Of course, if you want to shy away from the big brands, I didn't really help. But my suggestions are worth a look.