I will be traveling between Venice and Rome and between Florence and Rome by train. As I am looking at Trenitalia's website, I notice that there are several train stations. Which train stations do I choose for departures and arrivals for my trips when booking the trips?
Venice - Venezia Santa Lucia Florence - Firenze Santa Maria Novella (or SMN)
Rome - Roma Termini These are usually the first stations shown.
If you are staying in Venice proper (not Mestre) use Venezia S. Lucia. In Florence, Firenza S. M. N. (Santa Maria Novella) is the main station. Rome, all depends. Termini is the main station, but Tiburtina is a brand new big station only 4 subway stops from Termini and main station for the new Italo trains. Ostiensa is south of the city center and is also 4 subway stops from Termini. Trastevere is south of the Vatican and if your hotel is in this neighborhood, obviously it is a good choice.
Rome might be the only city on your list that has more than one convenient station, depending on where you are going. Trains leave from Termini for all the cities you mention, although the new Italo train company uses Roma Tiburtina. By the way, Tiburtina is not a new station. but it was largely rebuilt after a fire two years ago.
You can always choose " Tutti Stazione" for Rome. Mthen the Trenitalia website will route you to the correct one for your train.