Trying to sort this out, I see we can take the train from the port, and there are mini-vans to take you to the volcano's base. Is there a tour package that does this all inclusive for a reasonable price?
Many people will take a bus from the Naples port to the train station, and take the train out to Pompeii. It's the same train that takes travelers to the Amalfi Coast cities. You can visit Pompeii's sights and catch a van/tour to Vesuvius if you have time.
You could take the ship's guided tour, but at a very substantial price.
I have never used Viator tours (they're a third-party booker) but they do offer a Pompeii/Vesuvius combo tour from the port:
Do be aware that vans/buses can't take you all the way to the summit; they can only go so far and you have to hike the rest of the way. The path is rocky and loose, and you'll want to wear sturdy shoes. Note this text in the tour copy:
"...hop aboard your coach to Mt. Vesuvius for a 45-minute climb to the summit with your guide."
"A medium to high level of fitness is required to complete the climb."
The train ( Circumvesuviana) does not go to any Amalfi Coast towns, you have to transfer to the bus at Sorrento (Circumvesuviana's last stop). But it doesn't seem that you plan to go further than Vesuvius.
How much time do you have for this excursion? Is it a free day in port? If so, a guided tour may be the most efficient use of your time.
We toured Pompeii with pompeitour.com with Antonio Somma ..he was great..he is so informative and genuinely likes to share his knowledge . He was very patient and kind with our family of 7 . He met us at the train station and guided us to the highlights of Pompeii.. He made the city come alive and you could imagine life here in this city . I would highly recommend him . Thanks