We picked up a Budget Rental Car at a hotel in Santiago,don't remember the name but it was very large, a convention center, and located heading outside of downtown, easy access. www.budget.cl We rented from Hertz in Puerto Varas.
However, the most important thing I can tell you after renting cars in two locations in Chile is that no maps were given to us( not in Argentina either)We had a map of the country but it was not detailed enough and very long as you can imagine. Buy regional maps for your destinations before you leave on your trip. One rental car company gave us airport directions of "turn at church and keep going"..Luckily we did a dry run the day before, and there was a lot more information needed than that.
Also, they will tell you that if you get in an accident or anything happens to the car you have to report it to the local police immediately no matter where you are. We thought this meant an accident. A pebble dinged our windshield on the highway and we did not make a police report! When we turned the car in , we had to go to a Santiago police station, it was very crowded,and give the oral report in Spanish. We managed with the kindness of strangers. It would have been easier at a police station in the countryside where the windshield had been "dinged". Just a heads up. Chile is very into bureaucracy and paperwork which we experienced on three occassions. We have rented cars worldwide and this was the only time we had problems so just a heads up.
However, we loved the country, the best food we've ever had, fresh fish, vegetables and amazing fruits. Read Isabel Allende's "House of Spirits" before you leave.