As always, people have different definitions of "best."
From Naples to Sorrento, the cheapest is the Circumvesuviana train. It takes about an hour and is dirt cheap. No reservations; just go to the lower level of the Naples train station to buy tickets and get on. These run frequently. Some find them gritty, scary, crowded, or otherwise unpleasant; others don't mind.
At some times of the year, a few times a day, there is the Campagna Express. This runs on the same tracks as the regular Circumvesuviana, but makes only express stops, has more attendants on board, and is more expensive. So, it's designed to circumvent the problems of the Circumvesuviana.
There are ferries from Naples to Sorrento; you have to get from the train station to the ferry port, but then it's a pleasant ride.
Finally, there is the option of a taxi. This costs about €80 or so, but is definitely the easiest, and you get door to door service (if you take the train or ferry, you have to get from its terminus in Sorrento to your accommodation).
For getting from Sorrento to the Archeology Museum in Naples, once you get to the Naples train station, you can take the metro from the station to the museum. Or, of course, you can take a taxi all the way from Sorrento.