Local trains in Italy

These three towns are short train trips apart and there are many daily trains. I would not buy tickets in advance. There are ticket machines in the train stations where you can buy tickets for a few Euros; or you can buy your tickets at the ticket window. I doubt that reservations are needed or even available.

Don't be afraid to use the ticket machines in the stations, they are actually quite simple if you just take your time and follow the directions - you can select English as a language and use a credit/debit card. There are usually long slow lines at the ticket counters during the summer.

These are all short journeys. Very easy to buy point-to-point tickets at the train station or as suggested above, use the ticket machines. These will most likely be regional (R) or interregional (IR) trains. On these trains, there are no reservations. The ticket you get will be "open" which permits you to get on any train to the destination. No seat assignments either. No different from getting on the "EL" in Chicago. If there's a seat, you sit. If there's not, you stand. Almost always, you sit. It's really not bad. Don't forget to stamp your ticket at the little yellow box at each station before you board.

I get the impression you're using Lucca as a base and staying there a few days. At the train station it is quite easy to buy tickets; most towns have automated machines that let you do everything in english.

I've also used the machines for trip planning; I want to know when the trains the next few days leave so I don't show up at the station at 9am and find out the 8:50 train is gone and there's not another one for 2 hours. You can then choose to buy the ticket or return at the appropriate time and buy it then.

For our longer journeys, we had reserved seats and we noticed the train us much nicer, cleaner, etc. However, we ended up changing our plans, didn't use some advance purchased tickets and now have the hassle of trying to get refunds.