Another major rental spot is in the Bourghsee park (you take the escalator near the Spanish Steps up to all the auto rental agencies.)
We rented our car there, and using the directions furnished by the rental agency, it was easy to find our way out of town.
I have also heard that getting a car at the Termini worked well, also.
Don't rent a car without getting a GPS, or buy one here, learn how to use it, and take it with you.
Go to the autoeurope.com web site ( they are a broker that handles all of the major agencies. They are reccomended by travel agents and RS) Using their web site, plug in the different pick-up points and check out the varying prices and availablity of cars.
Also check to see if they have cars available on Sunday in Orvieto ( I am not excited asbout leaving luggage in a rental car.)