Best source/app for booking train travel in Italy

trenitalia and italo, the two companies. Trenitalia is the state run, Italo is private and only high speed trains. Both very handy!

Trenitalia is the Italian state train company: https://www.trenitalia.com/en.html

They have an app that let's you buy tickets and track trains in real times. Local regionale trains tickets need to be purchased 5 minutes before the train's scheduled departure and validated in the app before departure time to be valid. Fast trains come with assigned seats and don't require validation.
Use Italian city names - Roma, Firenze for best results.

.Italo is a private company that operates fast trains between big cities: https://www.italotreno.com/en
I believe they also have an app.

Fast train tickets can be purchased at a (sometimes large) discount ahead of time with limited flexibility so you will save money if you can sacrifice flexibility, but don't miss your train.

Have a great trip,
-Tod

My daughter used train line.com while studying in Florence (as recommended by her school). I'm sure the board will have opinions but her experience was all positive. They traveled by train every week for 5 months,

Trainline is a third party reseller
Nothing wrong with using it but they do charge a small fee and may not always offer all options

Some find the Trenitslia site difficult to use, I have no problem with it nor with their app
I mostly just use Trenitalia because it runs both fast and regional so all my tickets are in one place

I agree with Christine H. I have used multiple apps in the past but having all the tickets in Trenitalia is very convenient. I can also see where the trains are when in transit and get info on the platform, often before it is posted on the departure board in the train station which is handy if there are tight connections.

Thanks to all for the input. Much appreciated!