car rental at FCO

I go to Italy every year and use one of the two consolidators (both part of same corporate group):
www.autoeurope.com
www.kemwel.com
They work with the major rental companies: Europcar, Hertz, etc. (I generally choose the Europcar deals using those websites since it's cheaper with the full no deductible insurance option).
Try and see. However I can anticipate to you that renting one van costs as much as 3 economy cars, so you might want to split your group into 2 rental smaller vehicles (easier to maneuver in the narrow ancient Italian streets too).

We travel in Italy every year and we always use autoeurope.com. They are consolidators that work with a number car rental companies. Generally, usually, almost always, our rental through autoeurope is with europcar.com.

IMHO, purchase the zero deductible insurance for the added peace of mind.

Buon viaggio,

One important point to note is that each driver listed on the rental form must have the compulsory International Driver's Permit, which is used in conjunction with your home D.L. These are valid for one year, and easily obtained at any CAA/AAA office (two Passport-sized photos required, which may be provided by the issuing office).

You may also want to have a look at some of the other posts here concerning the dreaded Zona Traffico Limitato areas that are becoming increasingly prevalent in many Italian towns & cities especially Florence, which is almost saturated with automated ZTL cameras. EACH PASS through one of the automated Cameras will result in a €100+ ticket, which you won't know about until several months after you return home! This website provides more information - http://www.slowtrav.com/italy/driving/traffic_cameras_speeding.htm

There's also the issue of parking tickets, high fuel costs, tolls and automated speed cameras including the devious Traffic Tutor system which measures not only instantaneous speed but also average between two points. Violate either or both parameter and expensive tickets will follow.