Ask them a fixed price for the trip
some shuttles may require extra charges for waiting times and flight delays. Do not hire a taxi which charges hourly rates.
Do online research
Before you place a booking, do a little research with google.
Go their website and follow their social network links like google+, facebook and read some comments and reviews.
If they are on tripAdvisor, then see reviews about what people are saying.
Do not hurry to make pre-payments
If they suggest you to pay online immediately when you are booking, ask them what happen when you need to cancel or change your booking.
Be nice to the driver.
If you treat your driver well then he will also serve you very well.
Shared or Private [edited]
Ask them what kind of shuttles they have. There are two type of shuttles.
( thankyou superchief1 )
If You visit Disneyland Paris.
you may use Piyocab shuttle. They have low rates but a great service
Visit their website for more details : www.piyocab.com
Great tips. If it is a shuttle that stops at several hotels, I suggest checking the schedule to see how many stops prior to your hotel. I recall taking a shuttle from LGA several years ago that took over an hour longer due to my hotel being the last stop. The shuttle was full and I think most passengers were middle linebackers or nose tackles.