First time to Italy Advice - Roma, Napoli, and Amalfi...

That just depends on your list of things to do. No one will argue against a week in Rome!
For a shorter trip, I might suggest going to the coast first and putting all time in Rome together at the end--and there still be might be good reason to do that for better chance of good weather on the coast. I would consider booking something refundable in case you get rain. With a longer trip, I think it does make perfect sense to do your more intensive sightseeing in Rome first, then go to the coast, then return to Rome for at least a night before your flight home (sometimes it is fun to return to a place and see things you've missed or just relax).

Usually I'd say to go to Sorrento first and put all Rome at end to avoid that split stay. But since this is your first trip you might be better splitting Rome into 2 stays with Sorrento in the middle.

Looks like you have 14 nights? Is that right?
If so
Rome 4 or 5
Sorrento 6
Rome 3 or 4

Stay in 2 different areas in Rome-first somewhere near the Pantheon so you are very central to most major sites.
Second stay pick a different neighborhood- according to what your interests are. Trastevere would work for a different experience.
Planning your sightseeing to work well with those 2 diff locations will save you time/energy.

Keep in mind ferries won't be running in November- other than to Capri, Ischia, Naples? You will need to rely on SITA bus or private driver to get to Positano, etc.

Thanks for your input -

The day(s) we're traveling to and from Napoli, I've designated as, "Days off " so we can get used to the surroundings and relax.

Also, do you - other others recommend taking a taxi / private valet from the airport (FCO) to Rome, or take the Leonardo Express?

Rome to Naples, could not be easier, just a high speed train. From Naples to Sorrento is where I might consider splashing out for a private transfer, but there is a commuter train.
I would actually at least mull over spending a couple nights on Capri--you have a good amount of time, and a day trip is so different from an overnight.
Ferry schedules for Sorrento:
https://www.sorrentoinsider.com/en/ferry-schedule

A week in Rome would be fine, given the multitude of things to see and do. Your plans for Sorrento could be more problematic given the time of year . Some things will have closed for the season (like the AC ferries). Then you have the reduced daylight hours, cooler temp, and the increased probabilities of rain. I think you will want to keep your plans for these days as flexible as possible.
This site provides some perspective about weather averages over the last few years: https://weatherspark.com/m/76663/11/Average-Weather-in-November-in-Amalfi-Italy#:~:text=November%20Weather%20in%20Amalfi%20Italy,or%20exceeding%2063%C2%B0F.

Rick Steves says that there are four European cities that deserve a one week visit: London. Paris, Rome and Istanbul.

In Italy they have a saying: Roma, non basta una vita - For Rome, one lifetime is not enough.

From the introduction to The Smiles of Rome: A Literary Companion for Readers and Travelers (Susan Cahill, ed.)

Rome has the power to blow your mind and heart, bestowing a much larger capacity for the beauty of the world than you started out with… it’s the accumulation of pasts in Rome and one’s consciousness of those layers - in the city and in one’s self - that can make Rome a life-changing experience. Once Rome enters your consciousness, your perspective on human time may change, deepen, mellow… Everywhere, something invisible makes itself felt in the visible, making the whole city seem to pulsate with hidden presences, a register of the human psyche and of twenty-eight centuries of history striated by horror, by thrilling legends, and anonymous kindness. Getting to know Rome, we come home to ourselves…

Re: transfer from Rome airport. We took a pre-booked taxi on our first visit to Rome, but since then have used the Leonardo Express. We have stayed in hotels a short walk from Termini train station, the end point of the Leonardo Express. If you are staying a distance from Termini, you would have to take a taxi from the train station to your hotel, so in that case a taxi from the airport would be better.

A day trip to Florence would not be enough time to see much of anything. I would definitely reconsider that plan and think about spending a couple of nights.

Agree with the comment that November on the Amalfi Coast might not be ideal. Ferries will be spotty or not running based on the conditions. May want to cut that time there in half, and spend more time in Florence?