A transportation service is basically a shuttle service...like we used Seattle Express. They will tell you what time they will pick you up (or give you a choice of several times). You'll be in a van that may include other people. You may make another pick up or drop off on the way. But...the price is half or less what a "private" vehicle would cost.
For example, in Seattle we paid $12 per person and had a choice of 4 pick up times. I don't remember what the private limo/towncar was, but it was more than double (maybe even triple) this. OK, so we rode in a vehicle with 2 other pairs...bit deal? Not for us.
If you rent a car, you can also rent car seats. Budget charges $12 per day for car seats. If you decide to do a car rental, there are discount codes at rentalcodes.com and mousesavers.com.
If you book any kind of transportation service, limo/towncar/shuttle, or whatever, inquire in advance about car seats--many supply them at no extra charge. The airline will also fly them without counting them as a piece of luggage.