Help with train travel in Italy

Long answer short, you can't get there by train.

Lee, what say you?

Train to Naples from La Spezia via Florence and Rome is pretty straightforward.
Then you have some choices. Boat to Sorrento, then boat to Positano. Or Circumvesuviana to Sorrento, then boat to Positano. Or from Sorrento you could take the Amalfi coast Sita bus to Positano.

Or from Naples you can take the train to Salerno, then the Amalfi coast bus going in the opposite direction to Positano.

Those are all good choices. Boat to boat will give you the most scenery, boat to bus the most heart stopping "E" ticket ride, Circumvesuviana a chance to see how the other half lives and the thrill to experience changing trains and buying tickets in Naples.

Whatever you do, that's a pretty long day.

Have a great trip.

Thanks so much. Which choice is the quickest? Approx. how many hours will the whole trip take?
Which way would you go? We will have our 18 year old daughter with us. Is Positano a good choice of where to stay.

We will be there 3 days and then fly from Naples to Paris.

This is your fastest route from La Spezia Centrale to Napoli Centrale: Leave La Spezia at 06:51, change trains at Roma Termini, and arrive in Napoli at 11:25.

Go directly to the lower level of the station and buy tickets for the Circumvesuviana train to Sorrento. There's a chance you could catch the 11:40 train which arrives in Sorrento at 12:47. The next train leaves at 12:10 and arrives at 13:17.

If you arrive in Sorrento at 12:47, you should be able to catch the SITA bus to Positano which leaves at 13:00 and arrives at 13:50. If you arrive in Sorrento at 13:17, take the 13:30 bus which arrives in Positano at 14:10.

Assume you'll arrive in Positano at 14:10. If every connections works perfectly and you get there at 13:50, consider yourselves fortunate.

Thank you very much. We appreciate your advice!

We did end up taking the train from La Spezia to Rome and then to Naples. We took a taxi (cost 100 euros) from the Naples train station to Positano. It was so worth it! No dealing with luggage throughout the streets and hills of Positano. Also, was very quick (less than 90 minutes) and an air conditioned taxi! Took a taxi back to Naples after our visit in Positano too!

I would look into cheap flights from Florence or Milan to Naples. But if you're going by train (and then bus or ferry) you could do it, but it will be a long day spent mostly on transport. Also I'd recommend Sorrento over Positano since it is not only closer but a more central spot to do day trips to places like Pompeii or Herculaneum, Naples, Capri, the Amalfi coast, etc.