Be aware, there are two train main stations in Rome. The central one is Termini, but our high speed train to Florence left from Tiburtina. We almost missed it!
Definitely a good detail to reconfirm, maybe before going to bed the night before. When buying tickets, you should be able to choose between stations, for instance if you know your hotel is closer to Termini, but ways to do that vary by sales agent and may not be in very large print.
I prefer using Tiburtina instead of Termini, if the itinerary permits it. Tiburtina is only four Metro stops further east from Termini, and in my opinion it is overall a much more pleasant experience.
Ostiense is another viable alternative.
ed,
For future reference, there are more than two stations in Rome. As you found, Roma Termini and Roma Tiburtina are the most commonly used, but Roma Trastevere also handles passenger traffic.
I find Trastevere to be most convenient because of the #8 tram and where I usually stay around Campo di Fiori. It often requires that I take a regional to Tiburtina or Termini, but I don't mind.
Most European cities have more than one train station. In fact, I think Rome has at least four. Even Florence has two. You ticket should always indicate the station - both departing and arrival.
Roma Ostiense, down near Piramide metro stop, is the third big station near the city center.
There are seven or eight train stations in Roma, most tourists use Termini or Tiburtina.