letsgeaux

From the hotels on your list I would pick the Palazzo Murat. We did not stay there but we are familiar with it. It is a beautiful hotel right in the middle of town. It has a pool and a scenic courtyard. It seems to meet all of your criteria and it is an easy walk to the beach. You would do well to plan your day trips around the weather. We spent a week in Positano in April. We enjoyed Ravello and Capri very much, bht we did not go to the gardens in Ravello because it was cool and drizzly. We were in Capri on a beautiful sunny day but the Blue Grotto was closed due to rough seas. You will love the Amalfi Coast and the town of Positano.

Rubicund

The Palazzo Murat is not an easy walk down to he beach. The hotel, as mentioned earlier, is near the town end of the walkway down wide, shallow steps. To get down to the beach from the hotel entails walking down the walkway steps that do get steeper as you go down. We have stayed there.

letsgeaux

By easy walk to the beach, I meant near the beach as opposed to the hotels that are a ways up the hill. I consider anything in the small town center an easy walk to the beach. You don't have to walk via Pasatea or climb the steps that go up the hill.

Sassafrass

If you decide you want to see Pompeii, definitely do it from the AC, not Rome, and the easiest place to do that from is Sorrento. It is easy to get a taxi if you need it and you have plenty of hotels to choose from.
Views of the Bay of Naples from Sorrento are beautiful. You will not be cheating yourself by staying in Sorrento. Just choose the right hotel with a terrace and pool. Positano is gorgeous, but all the steps everywhere could well be problematic and make it not so enjoyable for you.

Micheline

In view of your mobility issues I feel you should rethink using Positano as a base. We loved it but the beach is very pebbly and very uncomfortable to sit on. The other beach is a good climb to get to. Perhaps Amalfi would be more suitable as it is flat and it's easier to get to Ravello from there.