I don't think it matters. From Rome FCO airport, you have to take a train to Rome Termini station and change for a train to Chiusi. From Rome CIA airport, you take a bus to Termini and then a train. From Florence airport, you take a bus to Florence Santa Maria Novella station, then a train.
You should be fine. Train stations have departure screens, similar to those at airports, headed "Partenze". These show the departure time, the train number (on your ticket for all fast trains), the final destination (which may be beyond where you are going to), and the platform (binario) that will be used.
I personally think Florence would be slightly easier but if there aren't any direct flights than you're stuck with FCO which, as Nick rightly points out, isn't that difficult either. My only comment having done it many times is that the train from FCO brings you into a platform 30 something whilst the Florence (ie Chiusi) trains go from a very low number (platform 7 or 5). A couple of trains in the mid afternoon even go from a platform about 400 yards down the street beyond platform 1, which is right over the opposite side of the station. Do ensure you have luggage with wheels. Possibly I'm dreaming but aren't there also announcements in English at Termini? There certainly are at Chiusi. Be ever so careful with your valuables at this station for it's notorious territory for pickpockets. There are slow trains and fast trains and the difference in time (and price) is considerable. Once you get to Chiusi, the bus station is just outside on the left. It's not far up to Sarteano, it's about 15 mins in the car and it's a really nice drive through olive groves with grogeous views once you get beyond the A1 intersection, but I'm not sure how frequent the bus is.
Have you looked at flying into Pisa airport? The Terravision bus or train to Florence and thence onward?
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