Seat reservations in Italy are mandatory in long distance trains and not necessary (and often not possible) in regional trains.
If you check www.trenitalia.com, you can choose if you want regional trains only or not. Regional trains for the summer have not been published yet; that could take another month. To get an idea of the timetable, check a date before 12 June. Some connections include an IC train, where a reservation is 3€. That can be booked at a ticket office or online via ÖBB (using these steps). There's no rush to book. A few days in advance is usually good enough.