I just bought tickets on line for Firenze-Venezia on the high speed train. We are traveling with another couple who fly to Florence on a different flight.
My tickets cost 58E for 2 people, one way leaving Florence at 4:30PM. Our friends booked their tickets on line at the same time, leaving Florence at 6:30PM for 38E (again one way).
So - moral of the story...if you know for certain you can catch a specific train and can plan ahead. I personally think it's a good idea to go ahead and get your tickets before you leave the US.
As I check the website, the fares continue to go UP as the date of departure approaches.
This is for the FAST train...I'm sure you can also grab any train and go for a less expensive fare....and maybe not have a seat to sit in for a few stops...etc.
We've traveled to Italy 10+ times now, rely on trains mostly, but have taken a few buses. Maybe 2x we got on a train and there were NO SEATS! It was loaded with people and suitcases. Not a fun journey, but we got to our destination.
As mentioned, if you do pre-purchase your ticket, you have to make that train, or your forfeit the ticket and there are no refunds. If you are flexible, then I don't see a reason why you couldn't plan ahead and get to the train station for a specific train.
Even when we are in Italy and plan to use the train the next day, we make a side trip to the station, purchase our tickets the day before so there is no rush at the station to get the tickets and find the track. (sometimes track number change too - make sure you double check the departure board, or ask as you board a train to make sure it's going to your correct destination)
Trains leave several times a day to the same destinations...some more directly/faster. Learn how to read the Departure board, your destination isn't always the LAST city on the route.