Advance Train Tickets?

It's not necessary, but it's cheaper. Just like it's not necessary to compare the prices of the 2 competing railway companies, but you can save money doing it.

On the other hand, full price tickets (called BASE or FLEX) do not sell out whereas discounted tickets can't be refunded and there are restrictions on changes. It's a matter of Flexibility vs money, your choice.

You certainly don't have to.

Unless you want tickets on the national day (and sometimes Fridays) there will always be available seats either on the train you want or on one just before or just after.

Many people buy on the day or just before travel.

What you won't find just before travel are any fares other than the most expensive.

We don't know much about you.

Do you like to plan or be flexible (code for change your mind at the last minute)?

Is it more important to you in this circumstance to save a lot of money or have flexibility?

You can do either but not both.

The decision is yours.

While you could save quite a bit by buying Rome to Naples, Rome to Bologna and Cinque Terre to Venice tickets in advance, the savings on the Pisa to Cinque Terre tickets would be small (around 5 euro per ticket). With that and the fact that regional trains don't take much longer in mind, you're probably better off waiting until you're ready to depart Pisa to buy those tickets. Buying your Naples to Rome tickets day of travel gives you maximum flexibility on what time to return but adds up to 26 euro per ticket to the cost. You'll have to decide whether flexibility or savings is more important.

If the time and route require a reservation I would consider purchasing in advance.

Looking for any experience and information on the train that runs the East Coast from Venice down to Bari. After arriving Sept/2019, and spending 2 days in Venice, we are going to hopefully take a scenic train ride from Venice that goes down the East Coast into Bari where my wife has some distant relatives. Looked on Google Maps and can see the train that runs and the time, not sure if it's a high-speed train or not? need for reservations? or what the cost would be?
Also would appreciate any input from taking the train from Rome to Siena up the West Coast via Grosseto? Thanks in advance for any input.

Peter, you have answers on your other thread with the same question.

Yes I noticed, thank you.

Thanks everyone for your insight! I think we will do advance tickets for a couple of the routes but probably not all.