Excellent information on Italian trains is here: Seat61.com. You will not be able to buy tickets for your time period yet.
To see the variation in fares, go to the Trenitalia website and price your trips for today or tomorrow and again for as far out as you can see fares (which might be in May; I'm not sure). If you know what day of the week you'll be traveling, use that day for your research.
There's a second rail company in Italy, Italo, that serves some of the major cities (not Sorrento). You may want to check its schedules and fares as well.
I'm not sure about Italo, but on the Trenitalia website you'll need to use the Italian station names:
Roma (Tutte Le Stazione)
Firenze S. M. Novella
Verona Porta Nuova
Venezia S. Lucia
You'll see that there's quite a range of travel time on most of your trips. The fastest, fanciest and costliest trains are the Freccia trains, which serve most major cities (not Sorrento, and I'm not sure about Verona). That's what nearly all travelers choose when they are available and convenient. The slowest trains are regionals, some of which stop at every station along the route.
I just look for a convenient departure time, then I compare the cost to the time in transit. Sometimes when you have to take part of the trip on a slower train (as you might into and out of Verona, depending on what time of day you want to travel), picking a routing that is partly on a Freccia train doesn't really save you any time (you might have a long layover somewhere) but does cost a lot more money.
In addition to the Trenitalia and Italo websites, there are European companies that sell rail tickets at approximately the standard cost (possibly with a small service fee). Some people choose to use them. They include loco2.com and trainline.eu. I would avoid RailEurope, which often doesn't display all the options (seeming to omit some less expensive ones) and frequently costs quite a lot more.