I'm male, 69, traveling alone on a budget.
Starting in Rome, working my way around to Palermo then to Palazzo Adriano. That's where my great grandfather was born and raised.
I'm looking for ideas of places I should see as I work my way south from Rome then up through Sicily.
You could definitely just do a week or so in Rome and then fly to Sicily and spend all of the remaining time there.
If you are set on the train journey down the mainland, then I like to look at the train map and see what appeals. You could easily spend another week+ in the Naples/Amalfi area, so decide on that first (and how much Rome time) to see exactly what you have to work with for Calabria. I have not been down that coastline south of Marina di Camerota, but Maratea (part of Basilicata) is a place on my list. Calabria info is less abundant but you can find info online--Tropea is very famous for example. It's based on if you are into beaches, nature, or history--should be easy to scope out good stops. good luck!
I love the beach, unfortunately I don't think the water will be warm enough. I like the idea of time in Naples, Amalfi. I've been in construction all my life. I love the architecture! Try to imagine how they built things with no power tools.
From Rome, you can take the train to Naples. It's a great place to explore on its own, and you’ll be close to both Pompeii and Herculaneum. From there, I recommend heading down to the Amalfi Coast. Salerno is a great budget-friendly base with easy access to the coastal towns.
To get to Sicily, you have a couple of good options: take a ferry from Salerno or Naples, or catch a short flight from Naples.
Once in Sicily, I recommend starting in Catania. It’s more affordable and well connected. You can do a day trip to Taormina from there; it’s a bit more upscale but absolutely beautiful. Then make your way south to Syracuse, which has an incredible mix of ancient ruins and seaside charm, and from there head to Agrigento to see the Valley of the Temples, one of the most impressive archaeological sites on the island. Finally, work your way over to Palermo, and then head inland to Palazzo Adriano.
This guide helped me figure out how to connect the Amalfi Coast and Sicily, in case it’s useful:
https://www.ferryhopper.com/en/blog/featured/amalfi-coast-sicily
If you plan to go to Naples, I suggest a stop at Caserta. The Royal Palace and grounds there are amazing as is the experience and history. It was very quiet while we were there in April. You could make a one night stay, enjoy the palace, have a nice dinner, and catch the train the next day.
We spent 4 nights in Caserta as a base. Also spent almost three weeks in Sicily a few years ago. Feel free to send me a PM if you have any questions.