As a newbie to Europe you chose the right place to start. Read, listen, learn from all the incredibly detailed information on this website ie. how to use transportation, where to walk, eat, shop, study, etc.
We have taken three Rick Steves tours and are scheduled again this spring. We have always extended our stays and use our learned knowledge to feel comfortable getting around on our own.
The Amalfi Coast is one of our favorite places. On different trips we traveled there by ferry boat from Sorrento to Capri, Amalfi, Positano. Another time we took the train from Naples to Salerno, then the ferry to Amalfi. In the other direction we took the bus back to Salerno, a beautiful coastal ride!
Ravello is stunning and we visited often. But we prefer to sleep by the sea. So on our last two trips we stayed at a small family run hotel in Amalfi Town called Hotel Floridiana https://www.hotelfloridiana.it/en/. They have comfortable rooms, delightful breakfast, and friendly staff. They also offer guided hikes to nearby areas including Ravello, the Path of the Gods, and the Valle Delle Ferriere which we enjoyed this past September. If you contact them ask which tours are in English – during the pandemic there was less need, so many tours were led in Italian.
From Amalfi town you can day trip by boat or bus to the other towns I mentioned above. Or you can hike! On a previous trip we luckily found, and have continued to use, this small book: “Walking on the Amalfi Coast” by Gillian Price, Cicerone press company. You can find it on Amazon. There are 32 walks centered in Ischia, Capri, Sorrento, Positano and Amalfi. We enjoyed hikes like Ravello to Amalfi via Valle del Dragone and Minori to Atrani to Amalfi. Just take the bus out and walk back! Be warned, lots of steps! Enjoy! Buses can get crowded, especially in high season. Get started early..
I left out one more transportation option, especially since I read about your kids. On our last trip we splurged and hired a limo ride to get us back to Naples. There are many good options from the Amalfi Coast to any of the big transportation hub cities.