trains

gabriela,

If a train requires reservations, those will be provided whether you buy tickets online or locally at stations. For travel on May 9th, I doubt that you'll be able to save much on tickets for the fast trains, as most of the Super Economy tickets may be sold out. If you'll be travelling on any Regionale trains, it's easier just to buy tickets for those in Italy, either from a Kiosk or at a staffed ticket office. DON'T forget to validate locally purchased Regionale tickets prior to boarding the train on the day of travel, or you'll risk hefty fines.

All tickets are available at the station and it sounds like that would be easier for you. Most lines have plenty of service and a whole train rarely sells out. See also https://www.ricksteves.com/travel-tips/transportation/trains/train-stations#buying-tickets.

All trains except the Regionale trains require a reservation and the total price is inclusive of everything. Only Regionale trains are open seating and it is smarter to buy those tickets at the train station at anytime.