Many people would take a private driver to the Naples rail station. You did not give the month of the year, which makes a huge difference. You have to deal with the fact that Frecciarossa tickets are not exchangeable or refundable, so you have to be on time. You chose to stay in a place that's a little hard to reach. I would never take the SITA bus (note that you did not explain whether you are before or after Amalfi town, where you have to change busses!) followed by the squalid Circumvesuviana train. Are you in a town where there might be HUNDREDS of steps between your hotel and the bus or taxi road? Some people write "best" when they mean "cheapest" or "fastest". "best" really is an opinion, and although you said you're not in a hurry, we don't really know your priorities. The ride from Amalfi town to Sorrento has nice views. The rest of the ride, either to Naples or Rome has forgettable views. You might have to specify the long ride with views if your driver knows a faster way to Naples, BTW. And you might have to pay extra for his time in traffic.
We paid our Sorrento hotel 95 Euros to drive us to the Naples rail station. It was money well spent, especially since we would have paid 15 Euros at least for a cab to the Circumvesuviana in Sorrento.