The one below is one that is very well rated, but you can Google NOLEGGIO CON CONDUCENTE followed by the name of the cities (FIUMICINO AEROPORTO SORRENTO) or even in English, AIRPORT TRANSFER and you will find many companies, the prices will range from €500 to €600 one way. If you rent a van for a day with return in Sorrento, I’m sure it will be less than half that including fuel and the tolls. The problem might be that you may not feel like driving jet lagged for almost 3 hours.
https://www.romecabs.com/italy-long-distance-transfers/
If you take the train the full price of a train ticket bought on the spot is approximately €62 one way per person to Naples. Then from Naples you would need either the commuter train (about €5 per person, or if you prefer a private car from the Napoli Centrale station to Sorrento, for about €80_100. So for 6 people the train doesn’t save you much and it adds to the hassle, so I would check whether a van rental is a viable option for you (cost plus the chore of driving) or otherwise go with a private transfer company.