what trains should I take from FCO airport to Orvieto?
Not sure what time of day you are arriving at FCO, but checked a date later in July and found you can take a train direct from FCO though you do have to change trains at Roma Tiburtina station and then on to Orvieto. Or you can take the Leonardo Express to Roma Termini and change to a train to Orvieto there. Either way the total time is about 2 hours. Shows anywhere from 1:50 to 2:16 total travel time, depending on which option you choose. Found all this on the trenialia.it site.
Actually it is trenitalia.com. Check the British flag in the upper right corner for English. No direct trains from the airport.