Edited - a few more questions - Early September Rome and Amalfi Coast

Unless you just especially want the experience of being in both Amalfi and Positano at night, you could choose one or the other. Paestum is difficult to visit from all of those locations, so you could look into doing it on a travel day, or swap for a base closer to the mainland end of the Amalfi coast, such as Salerno. You can take train north from Naples or Salerno.
Try to use ferry more than bus, to save some money on the private transfers. September is still high season, and you will likely want the respite of a hike to escape the villages.
You can visit Capri from Sorrento. Any interest in Pompeii?

Honestly, I just sort of threw a dart at the map to select bases, so all suggestions are welcome.

Yes, Pompeii is of interest.

Better to base in 1) Sorrento, 2) Positano or Amalfi, and 3) Salerno and visit Pompeii and Capri from Sorrento and Paestum from Salerno?

Definitely open to ferry travel vs private transfer or bus.

Read through the forum (tons of posts on this) to get a sense of the usual itineraries and think about how you want your days structured with the transport realities.

Can you afford $100+ for each car booking? This is an expensive area. Sorrento has the best public transportation. You don’t want to visit Pompeii from Amalfi, for example. There are no trains in Amalfi [town].

Don’t miss Ravello.

A number of years ago we trained from Rome to Sorrento, found a LOVELY small BnB type lodging right on the water (https://www.marinapiccola73.com/), within walking distance to the ferry. (Certainly not for the infirm! There is a trek uphill.) We easily used the ferry to travel to the gorgeous Capri, and the Amalfi coast. Check the ferry website to research all its stops. We LOVED it!

I would pick either Positano or Amalfi and spend 3 days on Capri.

We spent two weeks in Sorrento in 2023. Here's my Trip Report if you're interested. Due to chaotic and slow transportation issues in the region, I'd pick 2 locations max for your stays. Personally, we loved Capri much more than anything we saw in the Amalfi Coast.

https://community.ricksteves.com/travel-forum/trip-reports/trip-report-2-weeks-of-day-trips-from-sorrento

Personally I'd choose Sorrento on the one end, and either Amalfi or Salerno on the other; do Positano as a day trip via ferry. It's not very big, almost completely vertical, and doesn't offer much to do so I wouldn't spend 3 nights there.

From Sorrento: Capri, Positano, Pompeii.
From Salerno/Amalfi: Ravello, Paestum, other towns around the coast.

Transfer from Rome to Naples via high speed train, and to Sorrento via Circumvesuviana commuter train, ferry (would involve a cab or city bus to the port) or private driver.

Transfer from Sorrento to Amalfi or Salerno by ferry, bus or private driver. A word of caution: if you experience motion sickness, I don't recommend transfer by road unless you have an anti-nausea medication that you know works for you.

Thank you all for the great input - this forum never disappoints!
We are now leaning towards 3 nights in Sorrento, 2 nights on Capri, and 3 nights Salerno. So much to see and do - really looking forward to our trip!

We did Capri as a day trip from Sorrento, and I wished we had stayed over one night. Don’t miss Anacapri, a little quieter and less jammed with tourists than Capri. It has a marvelous church (S. Michele?) with a great ceramic tile floor depicting the Garden of Eden.
For your return voyage, be sure to allow adequate time to get to the proper dock. The last ferry of the day leaves pretty early; so, of course, it tends to be full.
As for Paestum, we discovered that we would need to go into Naples from where we were staying in Sorrento to get a train. The best arrangement for us was to book an all day bus tour. Pick-up was in Sorrento. The guide was good, and a stop in Salerno was included. It was quite a few years ago, so I don’t remember the price. However, I do recall that it was reasonable.

Don’t miss a visit to Paestum if you decide to stay in Salerno.

Think of trip in reverse
Suggestion: there is a direct train from Rome to Salerno, easy access to Paestum from there. Salerno is a wonderful town visit Minerva Gardens and Crypt of St Matteo in the Duomo. Ferry to Amalfi Coast from here.

Amalfi and Positano are shopping meccas and very crowded. Ravello is very popular and most people take the bus (very twisty) to Ravello. There are hiking steps up to Ravello( outside of Atrani) and yes it is a challenge, but I was 72 and not a hiker but fit. . There is a walking tunnel from Amalfi to Atrani.
I love Capri and highly recommend grabbing the bus or a taxi and going up to Anacapri, not into Capri town. Take the chair lift to the top and see an amazing view. We spent 2 nights on Capri and only once walked thru Capri town, it was mobbed! The hike to Villas can only be accessed from the Capri town side of the island.

From Capri you can easily travel to Sorrento back to Rome and on to Lucca.

Happy travels

Train to Sorrento - 3 nights Airbnb in Meta. Planning on a day trip to
Pompeii, Herculaneum and Vesuvius. Rick's guidebook says you can do
all three on the way from Naples to Sorrento, but can we really do all
three well in one day?

No, unlikely it is even possible on that travel day, though you could pick one. Not Vesuvius, because that requires booking. I’d consider Herculaneum, since it’s smaller, then do Pompeii on one of your full days. You have to really want to do the Vesuvius climb, I’m a hiker but was satisfied seeing it looming over the horizon,

Ferry to Positano, taxi to Ravello (Scala) - 3 nights apartment in
Scala. Hiking, hanging out and enjoying the views. Paestum from here
or better from Sorrento due to transportation options?

It is very difficult to get to Paestum from just about everywhere aside from Naples, Salerno, and the immediately adjacent villages to Salerno. It would be more realistic on the day you head to Sorrento from Rome, and that would still be a very long day. I think I’d give it a miss this time unfortunately.

Not sure why you’ve chosen Scala??

Valadelphia - I see that my post was a bit confusing. Rick's book suggests that all three are possible on the way from Naples to Sorrento but we plan on a full day to tackle them while we are staying in Sorrento. It still seems as though that might be too long a day. That said, I was planning on climbing Vesuvius and would appreciate knowing more about why you chose to skip that.

ChristineH - I was looking at lodging options in Ravello and an apartment in Scala with all of the amenities we were looking for showed up as an option. Thinking Ravello/Scala would be quieter than staying down in Amalfi or Positano.

Gotcha, in a full day, I’d say it’s a firm “maybe” but with a very early start, probably eminently “doable.” Keep in mind it will be very hot, all that rock and no shade makes Pompeii feel hotter than you would normally. Look at the scheduling details and the train times as you plan it out, but there would be no problem sitting them and doing one on each day (pair Herculaneum with Vesuvius), as you’d still have the long day into evening to do something else or just relax.
I just was not interested in the Vesuvius hike—it’s just so barren and if I’m hiking I want plants around me or a plunge in the sea at the end. Also you have to have a set time and that’s not my strong suit, lol. I might change my mind when I return one day—I have to get back to see Herculaneum and more of Naples.

we plan on a full day to tackle them while we are staying in Sorrento.
It still seems as though that might be too long a day.

You're right, it would be a very long day, and as someone else mentioned, you need a timed ticket for Vesuvius. I really wanted to do it, but ran out of time during our 2 week stay in Sorrento. I'm probably an oddball, but we ended up dedicating 3 days to Pompeii, Herculaneum and Oplontis because there was so much to see. We spent about 10 hours over 2 days in Pompeii. If I remember correctly in our trip planning we figured we needed a minimum half day and probably more including travel time from Sorrento if we were to visit Vesuvius. I regret that we didn't do it, but we'll be back to Naples at some point and will fit it in then.

Valadelphia - Since we are in Sorrento for a couple of full days and don't need to do day trips to Capri or the AC, I was thinking that the Pompeii/Herculaneum/Vesuvius visits might be best done as two day-trips instead of one rushed day. Very much into slower travel and having time to smell the roses, or the volcanic ash as it may be, rather than rushing and stressing too much. Thanks for the insights!

True it will be quieter but from what I remember no sea views-you are on the back side of the hill
Not much to Scala

ChristineH - The property listing states ocean view - photos confirm views from both the terrace and inside the apartment. I also looked at Google Maps and there are some more expansive views at the end of the block, so I think we will be happy there.

Re: your revisions. Is your stop in Positano to see the town? Amalfi is closest to Ravello, and with regular bus service up to the town. The private car/taxi… ymmv. For the most part, they’re going where the busses are going and in the same roads (and with the same traffic.) I found the views from the ferry to be a highlight of the experience. You’re actually getting better views from the sea versus the road. If your ride is more about the comfort for your group then I get that too.

You can effectively see Pompeii and Herculaneum in a full day. Get to Pompeii 1st thing. The majority of the site is around the entrance and forum, resist the temptation to walk to the amphitheater which is isolated. Take a good break for lunch, then see Herculaneum in late afternoon. It’s actually open until sunset I believe, so in season that’s quite late. Vesuvius is a bridge too far for one day, but you could combine that with time in Naples. Naples gets passed over a lot, but it has a lot to offer. The Archeological Museum is pretty essential.

Allan - Oh great, now I have to look up Oplontis and figure out if we need to see that too - LOL! Based on your input, as well as valadelphia's, I believe we will do Pompeii one day and Herculaneum and Vesuvius the next. Or vis-versa. Thanks!