Hi there, sounds fun! I'm not sure how 'tolerable' swimming will be at the beginning of October. I swam in Amalfi May 1st, it was chilly! Italians lined up on the beach to scold me for going into such cold water, then commented to each other, "oh, a FOREIGNER"! One alternative would be to pick somewhere to 'relax BY the beach' but also soak in thermal waters - IF the weather is good? Ischia comes to mind, if too cold to swim the thermal baths would still be fun.
In no particular order, just giving you some ideas here. What time does your flight arrive? If early enough, drop your suitcases at the train station and see Herculaneum on day of arrival? Herculaneum is easy to reach from downtown Naples, many people say it's a 2-3 hour visit.
You could hang out at the beach 2 days at beginning would be my preference because you want to be sure and make a ferry back to the mainland. Stay in a Naples hotel for convenience last 2 nights, take train to Paestum on Day 3 and go back to Naples for the night before your flight out? Not sure
I just posted a thread about week of Christmas in Pompei, (modern city across from entrance to ruins) visiting some things that interested you. Maybe some logistics are useful? Especially recommended tour guides. https://community.ricksteves.com/travel-forum/italy/ideas-about-our-trip-to-pompeii-naples-paestum