Train from Rome Fiumicino Airport to Civitavecchia

and rent a car there

Why? What's the benefit of not getting a rental car at the airport?

Anyway: www.trenitalia.com/en.htm

From: Fiumicino Aeroporto To: Civitavecchia

Day of travel: May 16 etc. Time of departure: As you prefer.

Click SEARCH.

There are other cities north of Rome like Viterbo, Orvieto and Chiusi where you could get by train and rent a car

Who gave you that information? We always rent cars at FCO, easy pick up and return. Civitavecchia is where cruise ships dock. Why would you go there unless getting on or off a ship?? That doesn’t make any sense at all.

But to answer your question, there are no trains from Fiumicino to Civitavecchia. You have to take a train into Rome and change to a train to Civitavecchia.

Who advised you to go to Civitavecchia? Probably someone who arrived with a cruise ship (Civitavecchia is the cruise port.

Going to Civitavecchia makes no sense in your case.

Rent a car at the airport, or at most in the city if the price is much better (a taxi from the airport to the city would add €50 fare to the cost).

For rental cars use AutoEurope.
They have 3 websites, check all three as the offers differ.

www.AutoEurope.eu
www.AutoEurope.com
www.Kemwel.com

As a pick up location use ROME ALL LOCATIONS and see the best price.
Select the airport location (most convenient for you) unless renting in the city saves you at least $100. I wouldn’t deal with the extra time, taxi money (50€), and the hassle of Rome city traffic for any less.

I believe the reason for not getting a rental car at the airport is that is difficult driving in traffic for someone who is not familiar with driving in Rome. We are from the US. Is the traffic and roads getting from the airport not so narrow and congested? We are not planning to drive into Rome. We are headed to Sienna, Italy from the airport.

FCO is well outside the city center

Use Google maps to see your route from FCO to Siena (note spelling)

You won’t be driving into Rome at all

In case you are staying inside Siena's ZTL on top of the hill, ask your hotel's concierge how to avoid fines.

PS Why should roads leading to an international airport be narrow? They weren't built by the Romans.

The airport is out of town and the freeway entrances are right there. No narrow roads to get to the freeway ramp.
However if you are going to Siena and you are afraid of narrow roads, you should rethink the entire plan to rent a car.