Rent a car: FCO, Ciampino, or Orvieto?

Take a look at renting your car at Ciampino airport and then dropping it off at FCO - you may find that there's no (or very little) price difference and it would make both ends of the rental easier for you. We did that 2 years ago through Hertz and there was no extra cost. You could also run the same pricing scenario with your 3rd option and dropping it off at FCO. Are you also going to be in Florence? If so, an option is take the train from Rome, see Florence, pick up a car there and then drop it off at FCO.

Thanks for the reply. No, we're not going to Florence. Is it easy to get from Rome to Ciampino?

Check prices on AutoEurope, a consolidator most of us use here. Check all their websites below, I also recommend you select the No Deductible Insurance Coverage option (a.k.a. Refundable Excess).
www.autoeurope.com
www.kemwel.com
www.autoeurope.eu

Select as pick up location:
ROME ALL LOCATIONS
Select as drop off location
ROME FIUMICINO LEONARDO DA VINCI AIRPORT (if you plan to spend the night at the airport) otherwise, if you don’t care, you can leave ROME ALL LOCATIONS as your drop off. The one way drop off fee is usually low (from 0€ to 25€).

Compare prices and make your choice.

Generally picking up at the airport (any airport) will cost more. Returning at the airport will not cost you more (except for a small one way drop off fee, if any). I generally return at FCO if I'm planning to spend the night at a hotel airport, but I rarely pick up at the Rome airport unless I plan to pick up immediately after landing and therefore picking up in the city would entail at least 50€ taxi fare. In your case, picking up in the city will almost certainly be cheaper than either airport.

I realize it takes time to search all of the options - I did it myself last year - but that’s the only way to get specific pricing for your dates.

Renting in a small town isn’t necessarily more expensive - it was roughly the same price for our trip - and a lot easier.