I will be traveling by train from Rome to Naples on September 18 2014. I will arrive at Naples Centrale at 1:55p. I will have about 45 minutes to get to the Molo Beverello ferry port for a 3pm ferry to Sorrento. Most likely I will take a taxi. I don't know the traffic in Naples. Will 45 minutes give me enough time to make it or would I be better off to take the 5:15 ferry?
It is only a couple of miles. In fact, you could walk across the plaza and catch a bus - no 1 as I remember. With the taxi, establish the fare before getting in.
Alibus runs from the train station to the port around every 20 minutes. Cost 3 euro
The R2 and the 202 also run between the two.
http://www.unicocampania.it/files/mappe/principali_collegamenti.pdf
I have not traveled this way through Naples, but according to Rick's Italy book, it looks like Tram #1 runs from Piazza Garibalidi in front of Napoli Centrale to the port (15 minutes, about 6x/hour, see pages 999-1001). Buy ticket at a tabacco shop and validate it as you board.
Oh man this takes me back! I did this very drive in a cab, all be it around 6pm vs. your earlier time and it is etched vividly into my memory. Yes, there will be traffic and yes you will make it in 45 minutes. How can this be possible you say? Well, because the cab driver will drive on the sidewalk and the opposite side of the road to avoid traffic!! It's the sort of cab ride you talk about decades later to your grand kids! Personally, I loved it!
Side note: While I've been burned by inconsistent buses in Italy too many times to fully recommend it, it's not a horrible suggestion either. If you're strapped for cash/don't enjoy the idea of the cab ride mentioned above, the bus might be a good option. I never bought tickets for the boats/ferries/hydrofoils until I got to the marina anyway so if you're late, just grab the later ferry and maybe a glass of wine while you wait. After all, the whole point of this part of Italy is to embrace il dolce far niente, no? Ok, maybe not in Naples, but once you hit the Islands, definitely!