From your previous post:
Our plan is to fly into Rome, then head north to Florence, Venice and
end in Milan (taking day trips from each major city).
How many NIGHTS will you have on the ground in Italy? That will give you a more accurate count.
But with what looks like two weeks to work with, you'll only really have time for the 4 cities with maybe one or two day trips. As already said above, passes don't usually work in Italy as well as in some other counties, and they don't work on Italo trains at all, should their schedules to some of the cities on your list be preferable to Trenitalia's.
For "fast" trains between Rome and Florence, Florence and Venice, and Venice and Milan, you'll want to use Trenitalia, Italy's national rail company, or Italo. Italo is a competative private line with very nice trains, and which operates almost exclusively between larger cites whereas Trenitalia also operates regionale trains between cities and smaller towns.
Here are their websites:
Buying in advance can land you some great price breaks, + the equivalent of 2nd class (lowest carriage tier) is perfectly fine but lowest-priced tickets usually lock you into a specific train at a specific time: no refunds or changes. The cost-savings are well worth it, though, and we've had no issues committing in advance to catching our trains. Even the most expensive full-priced/base priced tickets have certain restrictions.
A terrific primer for traveling by train in Italy is linked below. Just ignore the bit about ordering tickets through Italiarail as many here would recommend doing that direct via the websites above.
Many, many "short hop" day trips are done via inexpensive regionale trains, and ticket prices for those are the same whether bought in advance or not. For flexibility, you can just purchase them on the days of your journeys.