Need advise for Italy Trip...Train and public transportation

Just about everyone who's looked into this has advised that point-to-point tickets are the best way to go and a rail pass won't save you money. Switzerland is the exception in Europe.

Tickets for fast trains go on sale months in advance at big discounts. There are limited numbers available and the prices only go up as the dates near. For instance, you can buy a ticket from Rome to Florence for May for €30, for today at €50. The discounted tickets are no-refund, no-change. Regional trains are much slower and are cheaper - you can buy them on the day.

We used trenitalia Naples to Venice. I bought tickets before we left home for the best price. Easy to do, easy to use. But for the best prices it takes a some itinerary planning.

I had always prepurchased long-distance train tickets from home, usually Trenitalia, but on a recent trip with multiple shorter distances the flexibility of regionale buy-on-the-fly worked great (as long as you're not working against a strict deadline.) Just remember to VALIDATE the ticket before entering the train -- we watched several people (not Rick Steves readers, one must hope) who incurred large fines for using unvalidated tickets.
Don't try to cram everything into your first visit -- enjoy la dolce far niente (the sweetness of doing nothing.)

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:
https://www.trenitalia.com/en.html

https://www.italotreno.it/en

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.

https://www.seat61.com/Italy-trains.htm

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.

A site I like to use to figure out the public transportation from the train stations to your lodging is www.rome2rio.com. There’s usually a bus, tram or vaporetto boat in the case of Venice that’s handy, and this website will show you all of those options, plus the Italian name and spelling of the train station for using Trenitalia, etc.

pm,

I doubt that any Railpass will give you the "best bang for the buck" in Italy as tickets are relatively cheap there, especially for the Regionale trains. You may find this website helpful - https://www.seat61.com/Railpass-and-Eurail-pass-guide.htm (the section on "Point-to-Point tickets or Eurail Pass" should answer your questions).

A few points to keep in mind....

• Even with a Railpass, you'd have to pay out-of-pocket for the compulsory seat reservations on the express trains (Freccia, Intercity). If you're caught without a valid reservation for the train you're riding on, you'll face hefty fines which will be collected on the the spot.
• Railpasses are not accepted on all rail networks in Italy. I don't believe Italo Treno accepts passes.
• Railpasses will often be more expensive for travel on Regionale trains.

The method I normally use is to.....

• For trips on Regionale trains, I buy tickets locally either using a Kiosk or a staffed ticket office. The tickets are specific to the travel day and must be validated (time stamped) prior to boarding the train on the day of travel. Failure to do so may result in hefty fines.
• Tickets for Regionale trains can also be purchased online, and with this method they come pre-validated but the departure must be started within four hours of the time listed on the ticket.
• For trips on express trains or Italo, I buy tickets online well in advance. The Super Economy or Economy tickets are discounted, but if using that method the traveller MUST commit to a specific train, date and departure time as the tickets are valid only on that train. Note that the Super Economy tickets are non-refundable and non-changeable once purchased, and the Economy tickets also have restrictions.
• If you prefer to use the "spontaneous approach" and buy tickets as you go for the express trains, they will be more expensive as you'll likely be paying Base Fare, which is the highest price tier.