Massa Lubrense or Marina del Cantone?

Unless you were planning to have a car, for day trips, you'll have to take a bus or taxi to Sorrento every time. That may or may not be a consideration for you.
Here are some bus schedules: https://www.sorrentoinsider.com/en/sorrento-to-positano-bus-schedule?route=sorrento_sagata#section-schedule-result
I am not seeing the schedule for Marina del Cantone, but I am sure there is one.
Make sure the location is such that you can walk to restaurants.

This is really good advice. Thank you.

Figured something out (I want to get to this tip of the Sorrentine peninsula one day to do some hiking, hence my particular interest in scoping this out!): On bus schedules, look for "Nerano Cantone." It's this schedule:
https://www.sorrentoinsider.com/en/sorrento-to-positano-bus-schedule?route=nerano_sorrento#section-schedule-result
So, less convenient than Massa Lubrense perhaps, but looks to be a nicer beach.

I am not suggesting a car would be a problem-solver, just to clarify (you'd need a large one to fit all of you, the driving itself is windy, parking is expensive, traffic in summer), it is just that transport would be my first thought after being to the Amalfi side.
If you are looking for someplace less expensive and crowded than Sorrento, Positano, or Amalfi, the mainland-end villages of the Amalfi side are also nice. Anything from Minori to Vietri sul Mar is more relaxed and has ferry service, making day trips easier.
https://www.travelmar.it/en/index
If anyone gets motion sickness on a bus, this is a serious consideration.
You can get to Pompeii from this area, you'd just go to the Trenitalia stop instead of the Circumvesuviana one.

One thing to read about beaches is the direction of the sun--you might not want one that is shaded at the times you'd be there, that kind of thing.

Okay, you've convinced me. I am going to scrap these two places and look around Maiori or Minori.
I have discovered I misjudged geography and neither Massa Lubrense nor Marina del Cantone are actually on the Amalfi Coast!
Am now frantically scouring the internet where to stay.

That happens a lot! But some people really do want to just get away from it all, in which case it would make sense.
I stayed in pretty little Cetara, and while the beach was nothing to write home about, the restaurant selection was a plus--but likely has fewer rentals.
Vietri and the "M" towns are larger and probably have better rental selections, and Vietri also has a train station. I always confuse Minori and Maiori in my memory, but both have a beach that would be great for the kids, also the hiking route to Amalfi is super accessible (walk one way, ferry back--I think an eight-year-old could handle it). Minori has the famous pastry shop Sal de Riso.
That ferry was not operating from these towns when I was there and it's a real game changer--easy to hop over to Amalfi but much more quiet. From this area of the coast, you could also add in a day trip to the Greek temples at Paestum, which is too far from Sorrento and highly recommended.

@ Jeno

23/ 24 September 2010, two brothers-in-law, my wife and I stayed at agriturismo La Lobra, Massa Lubrense for the two nights.

24th. Took an early ferry over to Capri and did the tourist boat circumnavigation of the island. Lunch @ Lo Lodica (typical cheap pizza for tourist consumption). Returned and spent afternoon wondering the back alleys of Sorrento. Dropped in on a church, just off Piazza Tasso to catch the end of a wedding service. The wedding couple did not mind. A unique photo op. Had an enjoyable rabbit stew evening meal with the family. Rabbits bred on the Farm. Great day.

This was an area in Italy where I had no mates or acquaintances. We were on our own. The host family were nice to us, especially considering that I lost the key to my room somewhere during our trip to Capri. I had learnt my Italian from friends mostly from the north and central Italy. Different dialect south of Naples. So that was fun.

We rented a Ford Mondeo at Ciampino airport in Rome. Unlike many, we view driving in Italy as fun. Good and bad. A brother-in-law picked up a ZTL in Pisa, only because he was stupid. As Frankie Valli sang “only fools” get caught. For the day trip to Capri, we parked the car on a green near the Marina Picola. Cannot remember the exact details or price. Took a parking bay in Sorrento town for a couple of hours. I can read the parking signs. Driving in the region can be daunting for some. Finding an address can be tricky as many streets with the same name can be found in the various small villages.

Went to Pompeii next day. Had been a massive thunderstorm around 6am, so we got free admission which included the map of the site. I enjoyed our time there. I would classify the beaches I saw from Sorrento and along the Amalfi coastal villages as disappointing.

I would suggest going to this area one really needs to have the Lewis and Clark attitude as opposed to following in the footsteps of others. I see that you have updated your thoughts to the more traditional Amalfi villages. Could be a good decision. Others will not doubt let you know their experiences and pros and cons on weather, which is a big concern of many. Hope it all works out well for you.

Regards Ron

Thank you, Ron. Your brother-in-law sounds like my kind of fun.