Train stations are correct.
The following segments are on high speed trains:
Venezia S.Lucia-Firenze SMN
Firenze SMN-Napoli C.
Napoli C.-Roma T.
There are still discounted tickets (SuperEconomy and Economy) for those portions in September if you pre-purchase online.
However discounted tickets are non refundable and non changeable (the Economy can be changed but only once).
If you have absolutely firm plans on your day and time of travel you could take advantage of the discounts and buy those tickets now.
If you want flexibility to change your mind, then you can buy on the day of travel or the day before at the station.
To look at the schedule and if you want to purchase go to:
www.trenitalia.com
Since you arrive to Napoli by train, I think the Circumvesuviana commuter train is a better option, because with the boat you need to take a taxi/bus from the station to the port (Molo Beverello = Beverello Pier) and transfer to the boat. If you take the Circuvesuviana you are already at the station (you just have to go downstairs).
The circuvesuviana website is here:
http://www.eavsrl.it/web/en
From Sorrento back to Rome there is also a comfortable bus option, with the Marozzi bus company, which takes you to the Tiburtina station.
http://www.marozzivt.it/web.aspx
(click on "prenota Marozzi" to book, then 'ricerca orari corse' to see schedule or "prenota" to book)
The bus is slower than the train, but you don't have to deal with train changes and the luggage.