A few thoughts to add....
As the others have mentioned, rail passes are rarely cost effective in Italy. One point to note is that passes do not include the compulsory seat reservation fees on the express (fast) trains), and I don't believe Italo Treno accepts passes (should you choose to use them on some routes).
It's important to know which type of train you're using on each trip, and the rules that apply. You can easily buy tickets for Regionale trains from a ticket office or from the convenient kiosks in the station, which have English language menus. However, with locally purchased tickets, you must validate them prior to boarding the train on the day of travel or you'll risk hefty fines which will be collected on the spot (those are usually about 50€ PP).
Validating tickets also applies if using Metro or Buses in Rome. If you're going to be using public transit a lot in Rome, there are multi-day passes available, and those only have to be validated on the first use.
If you're using the express / fast trains such as the Freccia trains, those come with compulsory seat reservations which are specific to train, date and departure time. You must board the train listed on your ticket, or again you'll be subject to hefty fines and sit in the assigned seats.
As mentioned above, you could also use Italo Treno if their schedule works better for you. They operate a competing high speed service but no Regionale-equivalent trains, and again they have compulsory seat reservations. Their trains are a maroon colour so easy to distinguish from Trenitalia.
It would be a good idea to plan each of your trips so that you know the specifics of each train you'll be using.