Which train booking site in Italy

You didn’t say which cities you’re traveling to/between. Assuming it’s not on regional trains, use Trenilatila website so you book direct. Trainline is a 3rd party vendor. Someone can correct me if I’m wrong, but I don’t think the summer discount rates are out yet so it’s too early to book.

On OMIO I get it's too early to book. On Trainline

Why are you using re-sellers' sites? There are two competing companies running trains in Italy: www.trenitalia.com/en.html and www.italotreno.it/en Stick with the official sites and you won't have nasty surprises at the station.

which is it?

For obvious reasons, Nobody can sell you a ticket before the companies that run the trains. They are selling you a promise to buy in your name, at a fee.

some places changes their schedules during certain periods.

All European railway systems update their schedules twice an year, on the second Sunday of June and December.

This doesn't mean that you run the risk of buying a ticket for a train that won't run. When Trenitalia and Italo sell tickets for trains running after June 14 those trains will run: a timetable change means that by June they will gradually add more and more trains running between June 14 and December 13, 2020 until the new summer schedules will be fully uploaded.

You're best to book directly with the train company itself, either Trenitalia or Italotreno. Generally, train tickets won't be available yet for the summer, but probably will be by next month. If it's not on the company's own website, don't trust the schedule. The website The Man in Seat 61 has some great info on traveling by train in Italy (and elsewhere), including things like the difference between classes of tickets, etc.

There is a schedule change on June 13; some schedules not loaded until the next day.

I agree that The website The Man in Seat 61 is terrific. Thanks to Chiara for letting me know about it.

One more. One for the Trenitalia website. Easy to use.

Italiarail is the most user friendly website I found (I just booked all my Italy regionals there)

Italiarail is a re-seller, which means you may be paying more for tickets purchased there than you would on the websites of the companies operating the trains:

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

There are no benefits to buy Regionale train tickets in advanced. In fact, one lose the flexibilty and money if he/she needs to cancel the trip on the traveling day because of weather or a change of mind.

Italiarail is the most user friendly website I found

I'm afraid ItaliaRail is the most user friendly site because it uses English city names, it doesn't force people to check where the train stations are and because it sells combined tickets from competing companies in a single transaction.

In the real world, this means that you'll have to get used to Italian names while looking at the departure boards inside crowded stations.

More, you could end up not going to the city center, think at the direct airport train that in the evening goes from FCO to Florence Campo di Marte station instead of SM Novella; but the worst part is not having protected connections when the first train is delayed and the second one is run by the competitor.

there are no benefits to buy Regionale train tickets in advance

A regionale ticket purchased online doesn't need to be validated before getting on the train. Some think it's a good argument to avoid ticket machines and manned booths. I think it's the main reason to buy Regionale tickets online 15 minutes before getting on the train.

all great answers - I'd just add that Trenitalia has an app. It will only take Italian place names but you can check train times AND book tickets. I haven't used it yet but was looking at it last week and it seemed well built and easy to use - as indeed is the website.

On Apple: https://apps.apple.com/gb/app/trenitalia/id331050847

On Android: https://play.google.com/store/apps/details?hl=en_GB