Rebuilt will still allow you insurance, it's just rebuilding the motor. Rebuilt is actually better to buy, as it guarantees some new parts.

Salvaged vehicles....you want to check out the car from every single aspect, search every single nook and cranny in that car. Sometimes when they repair them they cut corners and you won't find out about it for quite some time, leaving you fucked over when you realize your car is about to fall apart.