In Italy, you have to buy seat-reservations for nearly all Trains:

- Frecciarossa, Frecciargento and Frecciabianca (10 Euros)

- Intercity and IntercityNotte (3 Euros)

- and Italo-Trains are not covered by Interrail 

Only Regionale (R) / RegionaleVeloce (RV) trains are covered by Interrail without mandatory seat reservation. 

So my choise:

- If you want to use Regionale/Regionale Veloce Trains, buy this Ticket: https://www.trenitalia.com/it/treni_regionali/promo-italia-in-tour.html

- If you want to use High-Speed Trains, buy Italo Tickets one-two weeks in advance (there are cheap tickets, for example Milan - Naples for 25 Euros)

- If you want to use InterCityNotte trains, buy Super-Economy Tickets with a 30% discount (wich code you find on Twitter -> @lefrecce). Buy tickets two weeks in advance. 

Also note that in various regions (Toscane=Firenze, Alto Adige) all trains are now run by a local/regional company and these do not take these passes. As you study I assume you wont be able to cover long distance daily, but make some weekendtrips. First get acquainted locally, ask around, if you study ITalian a good way is to learn all the sometimes quite hidden bargains by talking to local stuents-they will know best!

SAD in Alto Adige/Südtirol (not included) ,Toscana should be all of Trenitalia = Eurail valid

All regional trains that are run by Trenitalia, Trenitalia Tper, FUC (only Micotra services Udine-Villach) and Trenord (except Malpensa Express) you can use with Eurail without reservations (only hop on the train).

Malpensa Express to Malpensa Airport in Milan is not included, and the Leonardo Express to Fiumicino Airport in Rome is only valid with 1st class ticket. 

For Trenitalia Tper, I tried to find out 1.5 years ago but didn't find any information about validity on the lines formerly run by TPER. So do I understand correctly that these are also included?