Fiumicino suits an onward route into Lazio, Umbria or Tuscany. If you are visiting Rome first, compare travelling into the city without a car and collecting only when you leave for the countryside.
Renting a car makes sense for countryside stays, smaller villages and routes through the lakes or rural regions. For Rome, Milan and other major city stays, compare rail and local transport before paying for a car and overnight parking.
Compare airport collection with a later collection if you start with a city stay. Include the transport to a different rental branch and any extra parking nights when comparing the total cost.