You can put your luggage in the Naples train station. They have a left luggage room. You can safely take the commuter train to Sorrento, no problem. But if you prefer the hydrofoil, you can do that to. It is not unsafe to the take the Naples subway system down to the docks, but it is just simpler to take a taxi, which you can find outside the train station. They are all metered.

"They are all metered" but meter is not always turned on - keep an eye out.

Thanks!

Zeppole, do you think it is practical/do-able to leave our luggage at the left luggage room at the train station, go explore for the day, go back to get it, and then go back to the hydrofoil? Or do you think at that point it makes more sense to take the CV to Sorrento?

The left luggage counter at Napoli Terminale is straightforward and secure: you interact with a human being, who checks your passport and I think tickets before checking them in. Once you're luggage-free, you can take the subway to another part of the city, or start your wandering outside the doors of the station...

My experience navigating Naples with luggage was that we arrived via ferry from Sicily, then had to get from the docks to the train station. There's a bus that circles from airport to train station to docks, but due to construction in the area at the time, the stop had been relocated. Once we found it, it was a good way to get between the two (docks and station).

As for getting out to Sorrento, the Circumvesuviana is the most straightforward when you'll already be at the train station. But of course it's a lot less picturesque! The CV is a commuter train, and as such doesn't really have accommodation for luggage. Some cars have an area at each end, but often no seats adjacent...

The Fodorite A_Brit_in_Ischia had a post last year with a detailed explanation - with photos! - of transferring between the intercity trains and the CV, and he often posts about transportation in the area.

Which transportation method you choose - commuter train or hydrofoil - might also depend on:
* Where your lodging is in Sorrento. If near the water/downhill, it will be more convenient from the hydrofoil. If in the central area of town, then the train station will be. Don't forget, the town can be very steep in places!
* What you plan on doing in Naples. If you want to have dinner there, my experience was that you'll be hard pressed to find a restaurant that starts serving before 8pm. We were able to catch the CV after that, but do check schedules.