This answer only pertains to train tickets for travel within Italy.
You can certainly buy your train tickets online ( up to 120 days in advance) to take advantage of discounted ticket prices.
You can check train schedules, and book your tickets, on trenitalia.com for your travel within Italy.
All high- speed trains (Freccias and Intercity) tickets come with seat reservations.
Please note: Some of your routes involve taking Regionale trains which do not come with seat reservations; which means that there's open seating and one can sit in any available seat.
You can buy these tickets when you get to Italy, as there's no price advantage when bought in advance.
Enjoy your trip!
Edit to add...
One more thing I forgot to mention. You'll need to validate (date/time stamp) your Regionale train tickets prior to boarding the train to avoid expensive fines.
Just wondering.... Do you plan to visit Florence? Your journey from Venice to Perugia will be long and will most likely involve a train change in Florence.