score:9
Trenitalia.com is indeed the right site to book the tickets for your trip. If you book online, you receive an electronic ticket. All you need is an e-mail address and a printer to print out your tickets.
The system will usually show you several prices: 1st class, 2nd class, flexible, restrictive, special deals, ... Note that all else being equal, the cheaper tickets tend to be more restrictive. Check the conditions before booking.
The Italy page at seat61.com is highly recommended.
Upvote:2
There are usually trains leaving every couple of hours for your train service.
While booking in advance is nice, this is one of the few times I usually just pick up my ticket when I'm at the station. Trenitalia is the national rail service, and runs an express and a local. It sucks if you buy your ticket and miss your train, as it's a pain to change tickets, but if you buy when you're there, you can always just get on the one that's leaving next.
Enjoy Italy!