Santorini Airport is a very busy but small airport serving more than 400.000 passengers per year. Getting a private or a shared transfer at is a good choice, but remember to pre-book it in advance to avoid long queues at the arrivals terminal.
If you do not want to rent a car, then a very good choice is to book a private or shared transfer to your hotel.
Here is a licensed company that offers transfers from and to the airport.
Santorini Transport: Shared and private transfers. Door to door pick-up/ drop-off direct to your accommodation.