Just received this tidbit in an email from my Rome contact.
For the car, you could just go to the Concora booth, though lately we've been using Gianesi because they are more reliable and also cheaper (40 Euros from the airport vs 60 for Concora). They don't have a stand at the airport, but if you send them an email with your flight info they'll have a car waiting for you when you arrive (website: www.gianesibus.it ;email: [email protected]).
This organization has lots of people going back and forth to FCO weekly, so I trust them.
In the past, we used Concora, but we're happy to experiment.
We're scheduled to come in during the March 18th general strike

, so instead of the usual fco-trastevere train connecting to the tram a little walk, we'll probably take the car service.
lala