First, have you booked your flights yet? If not, try to fly into Naples and out of Pisa or Genoa. It may cost a bit more, or it may not, but you'll save time and money by not having extra travel to be at your start and end points.
If you use Naples as your base, then Capri, Sorrento, Pompeii and Herculaneum are easy day trips. Further afield to places like Positano or Amalfi are not. That's why the usual advice is to base in Sorrento. The other reason is that some find Naples overwhelming; I liked it. One thing I didn't enjoy was my daytrip from Naples to Sorrento and Positano - these are places to linger, not fly through, so it was a waste of a day.
If you are locked into flying in and out of Rome, you will not need a night in Rome on the way in, but will almost certainly need one on the way out. Getting from the Cinque Terre to FCO will take about 4 hours, and unless you have an unusually late flight, you won't have time to go through security and make your plane if you try to do this all in one day. However, on the way in, you can get a train to Roma Termini and then a train to Napoli Centrale; these trains are very frequent, so there's no need to stay in Rome that night unless you wish to. Getting to Sorrento from Naples requires yet another train (I don't know if the boats are still running in October). If you fly into Naples airport, getting to either Naples or Sorrento is by direct bus, so it's a "one seat ride."
You can get a tour guide if you wish (many do this for Pompeii, for example), but it's not necessary anywhere. In the places you're going, there will be enough English spoken for your needs.