FCO to sienna

Take the train into the Rome Temini.
Take a regional train to Orvieto--70 minutes.
Pickup a car across the street from the Orvieto train station at Hertz Rent a Car.
It's about a 90 minute drive up to Siena--all motorway (toll) and 4 lane highway.

If you went by train, you'd have to go up to Florence, and transfer to a train that drops you off on the edge of Siena. The bus is the preferred way to get to Siena from across the street at the Florence train station.

While in Orvieto, it'd be a great place to tour and spend the night. It's a very popular tourist stop hill town.

Best is subjective. Some people might love to travel the slowest and least economical way.
Do you intend to rent a car once in Siena? If you do, you might as well do it from the start. The drive from FCO to Siena is less than 3 hours (all freeway).
If you opt for public transportation, you can take a train from the Airport to Rome Termini (main) station. From there you would take a train to Chiusi, then another train from Chiusi to Siena. Or you could take a fast train to Florence, then a bus (or a train) from Florence to Siena.
Another option is the bus. You would need to take a train to the Roma Tiburtina Station, then from there take a Sena Bus to Siena.
Train schedules here:
www.trenitalia.com (departure station is Fiumicino Aeroporto, arrival is Siena. Choose a date in the next 7 days).
The bus schedule from Roma Tiburtina to Siena is here:
http://www.sena.it/Home/78-1-en.html

Thank you both very much.
We want a place to stay for 3 nights before headed to rome,
and we will get a car for those three nights but would prefer
not to drive out of Rome. So would you suggest Orvieta over Sienna?
Thanks again.
Susan