1.)
Yamaha Pac 112 -nice small neck,very tough contruction and electronics,get a painted one as the bodies are tougher, i have a natural finished one and its as soft as a bolied egg.
2.) Cort Cl 100/200 Les Paul ish and excellent for the money.
If you play already :A Yamaha S(B)G or one of the faded Gibsons,will see you right, -probably too expensive if you're not sure you want to keep on playing the guitar.
In the end it's up to you -get what your hand can "fit",will make a long note *without* being plugged in and do TRY to ignore the name on the headstock,let your ears decide.
Accuracy,you say? hmm interesting concept..