Italy's rail network connects the cities you are probably going to anyway, and the measured times on this page show why driving between them is rarely worth it: Rome to Naples in seventy minutes, Rome to Florence in ninety, Florence to Venice in two hours and Milan to Venice in two and a half. Fourteen journeys are bookable here, from six starting cities.
Two operators run the fast trains. Trenitalia is the national company; Italo is a private high-speed competitor on the same main lines. Both require a seat reservation on high-speed services, and both are substantially cheaper booked ahead than on the day, so the choice is usually made by departure time rather than by brand.
Not everything on this page is high-speed, and that is worth knowing before you compare durations. Naples to Sorrento is a regional line — slower, more local, and the way to the Amalfi Coast. Palermo to Catania is a Sicilian regional run. And Rome to Catania is an overnight service on which the train itself boards a ferry to cross the Strait of Messina.