One of the best car rentals on the island is Vazeos car rental. Panagiotis, the owner is really professional on that business. Many types of new cars, transfer and pick up services and the same time, with really reasonable prices. Safety is maby the most important criteria when you rent a car. Feel free to rent from Vazeos. All the cars they have are double checked for their safety.
We rented a cabrio BMW, just with a call. The staff that brought the car to our hotel was so kind. At the end of the rental, we left it at the airport!
Passing from their office in Oia, we saw also luxury cars, wedding cars and quads, atvs and buggies available for rental.
In any case, ask for Panagiotis. They offer really good quality car rental service.