Travel from Sienna to Sorrento

If you don't want to pay $260 a person then here is the best way:

This fastest most cost effective and convenient way is to take the bus Sienna to Rome.
https://www.itabus.it/en/tratte-bus/rome-siena

The bus drops you outside Rome Tiburtina train station where you can catch a train to Naples
Roma Tuburtina to Napoli Centrale
https://www.trenitalia.com/en.html

Change in Naples for the Campania Express :
https://www.sorrentoinsider.com/en/campania-express-train-schedule

or the Circumvesuviana (this is cash only local commuter train)
https://www.sorrentoinsider.com/en/naples-to-sorrento-train-schedule

to Sorrento.

$260pp seems like a heck of a deal in terms of convenience. Have you priced it a rental that includes drop-off fees? It's a long day no matter the mode of transportation so with your own car at least you can stop and explore wherever you like. Or if you're looking to save money and some convenience, a car service to Florence and then trains?

Well it IS almost half the length of the country for the drive, and at the moment it says over 5 hours. I would say that's a good deal if you wanted a car and driver. BUT a train would be more comfortable for me, as I can get up and walk around, stretch my legs and not get stuck in traffic. I would prefer that as long as I could manage my luggage (I always want to chuck my carry on sized luggage off the train the second one we take haha) through the train changes. Renting a car would incur the toll road fees and then relegate the driver to keeping their eyes on the sometimes difficult coastal road instead of allowing them to take in the views on the way to Sorrento (ARE there views from the CV on the way to Sorrento? I have only ridden it twice and can't remember, either way, the tiny roads on the peninsula aren't fun).

Take the bus from Sienna center city to Florence. Walk across the street from the bus stop (by McDonalds) to the Florence train station.

Take a fast train down thru Rome Termini to Naples.

Catch a local train in Naples to Sorrento.

That doesn't even require much walking

I really doubt you would enjoy doing the drive yourselves. I would take the bus to Rome, train to Naples, and then possibly a private driver onward from there, which will be a minimal cost compared to the whole long journey.

The driver from Napoli to Sorrento is a perfect compromise, as Val said....that leg is the most "uncomfortable" (commuter train, possibly no a/c, no guarantee of a seat) and arriving in style would be awesome :)

Month and Year?

As noted, there is nothing pricey about the car quote. But if the car is an air-conditioned Mercedes sedan, a popular black car in this area, five people is a pretty tight fit for a five hour trip. Doesn’t sound so luxurious to me.

I haven’t checked but five Frecciarossa fast train tickets just from Rome to Naples could easily cost $200 in all. More from Florence. But that would depend on the time of day you’re traveling and how far in advance you buy the tickets, which then could be non-changeable & nonrefundable. These trains are so much faster than automobiles that there’s no question it’s worth the money.

You might want to do a little research on the Circumvesuviana train, because it’s so hot crowded and gritty that you might be willing to pay any amount of money to avoid it Including, $150 car service from Naples to Sorrento. Reports on this news board suggest that the Circumvesuviana service is installing tap and go terminals, but that hasn’t been verified yet.

When online researching, note that Siena has one “n” only.

How much luggage do you all have? If it's a lot, I'd hire the private driver. As others have said, you're going to have to make 3 transfers on public transit, and with luggage, that's a lot of hassle.

We recently took the train from Rome to Florence, 1st class ticket on high speed train for $120 for two.
The regional train from Florence to Siena was cheap, about $20 for two.
When I researched transport, bus service looked like the best, but I was put off because I didn't know when to pick it up, etc.

Thank you for all the replies. I agree with some, thinking the private driver is the way to go. Will be much easier than doing the "bad drag" on multiple trains.