From VCE airport to the historical center of Venice (in the middle of the Venetian lagoon), considering you'll be tired and jetlagged, there are 4 of you, including a child, I recommend a regular taxi (with wheels) to Piazzale Roma (the last point where cars can arrive) then a vaporetto (basically a water bus) to the location closest to your hotel (we need that info for more detailed advice). There is also the possibility of a water taxi from the airport to a dock close to your hotel, but that will cost you more (120euro). Another option is the Alilaguna boat service, which is the midprice option (http://www.alilaguna.it/en). But again it all depends on where your hotel is.
From Venice to Florence, you take a high speed train. Timetable and prices below (about 45euro pp, full fare, half price for the child):
www.trenitalia.com
The station names must be spelled in Italian:
VENEZIA SANTA LUCIA
FIRENZE SANTA MARIA NOVELLA.
To get from Florence to Ponte Buggianese, you would take a train to Montecatini (use Trenitalia website above for trains). Then you need a bus. That area is served by the Blubus company.
http://www.blubus.it/indice-linee.html
The line you need is the Montecatini-Altopascio-Lucca. The Montecatini train station is on Piazza Italia, the bus will be in front of the station. You could probably take a taxi at the Montecatini station to Ponte Buggianese as well (it's just 5 or 6 km). I wouldn't take a taxi/driver all the way from Florence (60 km away), that would be expensive, and believe you me, there is nothing to see in Ponte Buggianese. It's just a suburb with nothing worthwhile to see, other than your boyfriend's family (if you are visiting some). Montecatini however is a quaint spa resort town, which is a worthwhile day trip. Maybe you could spend most of the day there, and do a quick taxi run to see Ponte Buggianese.
You could also rent a car for a day from Florence, but I think the train to Montecatini plus taxi is faster, once you factor in the rental paperwork and rental return process (and getting lost driving there).
From Florence to Sorrento is a long trip (nearly 3 hours to Naples, then another hour to Sorrento)
First you need a high speed train from FIRENZE SANTA MARIA NOVELLA to NAPOLI CENTRALE (Naples).
Use the website above for the trains.
Then once at the Napoli station, you take a commuter train to Sorrento, called Circumvesuviana (website provided below):
www.eavsrl.it
To go back to Rome you do the reverse. Then in Napoli Centrale you take a train to ROMA TERMINI, Rome main station (use the trenitalia website above for train info).
You don't need to purchase train tickets in advance, you can buy on the spot at the station, seats don't sell out as there are many trains (one to four per hour), however if you pre purchase online in advance (tickets start selling online 120 days prior to travel date), you can secure discounted tickets called SUPER ECONOMY or ECONOMY fares. If you do so, be aware however those discounted tickets have restrictions, that is you will be locked on the specific train you buy. In other words no changes nor refunds are allowed. Supereconomy tickets allow for up to 40% discounts. The full fare one way on standard class (2nd class) is 45 euro per person from Venice to Florence. Naples to Rome is about the same. Florence to Naples is 75 euro.
From Florence to Montecatini, you don't need to buy in advance. Also no prepurchase on the Circumvesuviana from Naples to Sorrento. No discounts on regional commuter trains. Regional train tickets must be validated before boarding (date stamp at the machine). The high speed trains mentioned above, are train specific (like airplane tickets), so no validation necessary.
