Looking to go from Rome, to Lecce, to Matera, then Amalfi Coast and Naples. Prefer to drive as little as possible. Suggestions?

We are looking at a very similar trip so I'm interested in any replies to this. As we are going in January we are going to skip the Amalfi Coast. Our plan is to catch the train across from Rome to Lecce. From Lecce to Matera we are booking a transfer that includes a stop at Alberello. It's the Matera to Naples part that I am struggling with, and wondering if its easier to head from Matera to Bari and then catch a train. In your case you could then catch a train to Salerno from Naples.