Traveling from the port in Naples to Sorrento with a stop at Mt. Vesuvius and Pompeii

How many days are you staying in Sorrento?
Doing both stops en route from Naples might be too much, and since it is so easy to visit Pompeii from Sorrento, I would visit it from there rather than storing bags. The Vesuvius trip is a whole thing (a partially guided tour with transport), so best to google those details--there should be a place that will store luggage in Ercolano if you go that route though.

My advice- don't even think of trying to do both unless you enjoy heat stroke. At that time of year it is HOT, and there is no shelter from the sun. Either should be done as early as possible in the morning. There is luggage storage at the Pompeii Scavi site, but I don't know about the Vesuvius base. We were content to just look at it from a distance.

Sorry, my initial inquiry was not clear. We are going from the Naples port to Sorrento and staying three nights. We go to Positano for three nights after that. We were just wondering if we can visit Mt. Vesuvius and Pompeii on the way to Sorrento, rather than go back after checking into hotel.

Yes, we got that, just making sure you have some time in Sorrento, from which it will be much easier to take these trips unencumbered. Maybe one would be possible, but I have extreme doubts about doing both.

Do consider this:
https://community.ricksteves.com/travel-forum/italy/pompeii-and-vesuvius-69e8366c-1e75-4a14-a0bc-0677269492d1

Look at it this way: If you simply booked a black-car and driver from Naples to a Sorrento hotel, that would be 125-150 Euros, and take about an hour. (With good luck on the traffic.) So every hour you are paying someone to sit in the car and watch your bags is going to cost about 125 Euros more. How many stops do you want to make on the way to Sorrento, when you could do each of them as a public transit (commuter train) outing from your hotel in Sorrento? (Can't do from Positano.)

Heat and sun in midday are a BIG issue at both Pompeii and Vesuvius. Pompeii and Vesuvius are not adjacent, so extra time is involved with the car service. Please make sure your departure from Positano is realistic. You cannot fly home from Rome after waking up in Positano.

https://community.ricksteves.com/travel-forum/italy/naples-to-sorrento-train-or-private-driver

https://community.ricksteves.com/travel-forum/italy/getting-around-amalfi-coast

https://community.ricksteves.com/travel-forum/italy/how-do-i-get-from-pompeii-to-positano-is-there-a-direct-route

You can take a ferry from Naples port to Sorrento
That is the simplest most direct route

Much easier to visit Pompeii without luggage from Sorrento

If you must visit on the way then it’s a taxi to station then the commuter train to Pompeii-store your bags -then commuter train to Sorrento
This train is always hot and crowded and often SRO-very difficult with luggage

Not recommended

Or hire a private driver

We just visited that area but it was January, when the sunshine was very welcome! The best solution might be to arrange a private tour that can keep your luggage in the van and drop you off in Sorrento. I assume you’re not planning to rent a car in Naples? If you were then you could drive to those places yourself. Parking at Pompei would be in a private lot so I think your luggage would be okay. They challenge is parking at Mt Vesuvius - we got to the top and found out that only taxis and tour vehicles can park there. Everyone else had to go back down 1 km and park there, then walk back up or pay a taxi from there. And of course, on a Tuesday in January there were no taxis at that parking area (and only one car parked!). Anyway, good luck with the trip!

Thanks for everyone’s suggestions. We decided to take the ferry from the Naples port to Sorrento and then a taxi to the hotel. We will plan to go to Pompeii the next day. I’m not sure if we will book a tour or just take the train and buy tickets on our own. Any advice on this?