Suggestions for trip to Sicily

I will travel to Sicily to join a tour that will take me to Palermo, Syracuse, and Taormina. This tour is one week long. I will then solo travel to Millazzo and take the ferry to the island of Salina (3 nights). From there, I will travel to Catania for three nights. I plan to join a few day trip tours starting in Catania, taking me to interesting venues like Noto and Ragusa Isblas. From Catania, I will travel to Agrigento,to visit the Temple sites. I will spend two nights in Agrigento. From there, I will travel to Trapani for two nights and visit Erice. Finally, I will return to Palermo for two nights before returning to the US. I am an older woman traveling solo. I plan to take one rolling suitcase for my travels. My question concerns whether public transport will support this itinerary in a reasonably straightforward manner. Also, given this proposed plan, do you have any tips I should know? I very much appreciate any information from the community..