Train or Car from Rome to Sorrento

I would go with Train. Driving through Umbria or Tuscany would be great but I'm not sure it's worth it to go from Rome to Sorrento. You will love Sorrento - what a nice relaxing town! Take a day and go to Capri, if you have time.

Train. You will be just arriving after a long, tiring flight. The last thing you need is to be navigating Italian streets and roads. Take the train. You will be more relaxed, have time to take a nap and have a sandwich or meal on the train and avoid arriving all frazzled.

More than that, you will avoid the hassle of trying to find a place to park and navigating a city with which you are unfamiliar.

Train will be much easier...especially after you arrive in Sorrento and figure out that there's no place to park that car. Rental Cars in general just seem to be a pain in the neck in Europe...at least from my experiences. Luckily I kicked that habit long ago and only do trains now.

Take the Leonardo Express from Fiumicino to Roma Termini. Take a train from Termini to Napoli Centrale. You can buy both tickets at the airport station. Go to the lower level of the Napoli station and buy a ticket for the private Circumvesuviana commuter train to Sorrento. Trains are frequent and cheap.

We are 5 so we will drive (I like to drive and stop where I like). I will also use the car to go to Pompeii, Mt.V, Amalfi Coast, etc.
If it were 2 of us Id take the train.

The little commuter train passes right by the Pompeii Scavi entrance. If you took the train it would be super simple to get to Pompeii from Sorrento. I realize some people just like to drive. Not me, I'm a "train convert" these days!

Driving in the Amalfi coast is scary. I'd use the train and buses. Hiring a car and driver is pricey as they are all Mercedes.