The busses cost considerably less than jet flights. An airport shuttle will drop you at the Santiago bus terminal. There are several rental car agencies at the Puerto Montt airport. The rental agent asked to see my US driver's licence, passport and major credit card. Here is a commercial WWW page for Puerto Montt .
Some useful content is tucked in amongst the paid advertisements.
Puerto Montt is NOT the best place to stay overnight. It is industrialized, smoggy and congested. There are many well maintained, paved roads. However, a lot of interesting places are served only by gravel roads. The gravel roads can be good during dry seasons, or they can degenerate rapidly during wet weather.