Rail to Positano

We got a driver to take us from Naples train station to door of hotel and was worth every cent. I think it was 150 euro but we had a van as there was 5 of us.
Otherwise it’s the train to Sorrento then bus..

Trenitalia trains will only get you as far as Naples, or alternatively Salerno. From either of those points, you'll need to use either a private transfer or some mix of local train, ferry and bus to reach Positano. The most efficient route would be train to Naples and private transfer, but that's also the most expensive.

We took Frecciabianca train from Rome to Naples and then a car from Naples to Positano.

I personally would not combine CT with AC in one trip. But your choices after Naples are commuter train or bus to Sorrento, then bus or private car to Positano, or private car all the way from the Naples rail station. We had our hotel in Sorrento book their land partner to take us back to the Naples rail station on departure. We took the "gritty" Circumvesuviana train on the way in. It was jam-packed and hot. And we paid 15 Euros taxi to our hotel anyway.

The bus from Sorrento to Positano tends to be very crowded, but it's also very cheap. Some people use ferries, but the ferry routes start to decline in number and frequency after the end of September. Be sure you are looking at the right timetable.