Seeking Feedback on 2 Week Italy Itinerary

Hey fellow travelers! ✈️ My husband and I are planning a 2-week honeymoon in Italy, and I'd love your expert input on our itinerary. I've been to Italy many times, but it's my husband's first trip abroad, so I'm aiming for a mix of popular tourist spots and off-the-beaten-path gems.

A few things I had to take into account when creating our itinerary:

1. We want this trip to maximize how much we are seeing without feeling rushed and like we are constantly bouncing around, packing and unpacking our suitcases.
2. We must fly through either Milan or Rome to get the best deal on airfare
3. We must spend at least one day in Gioia Del Colle, where my husband's grandfather grew up.

Itinerary:
Day 1: Travel day, Fly from Newark to Rome overnight
Day 2: Land in Rome in the morning
Day 3-4: Explore Rome
Day 5: Travel from Rome to Amalfi Coast
Day 6-7: Amalfi Coast
Day 8: Travel from Amalfi Coast to the Puglia Region
Day 9-12: Explore Puglia Region
Day 13: Travel from Puglia Region back to Rome
Day 14: Fly from Rome back home

Questions:

1. Getting to Amalfi Coast: Train to Naples + bus or rent a car? Any recommendations?
2. Best Stay on Amalfi Coast: Any suggestions for accommodations? Where would be the best jumping off point to give us the best options for day trips, etc. Should we consider Ischia island for a more "off the beaten path" vibe?
3. Traveling from Amalfi to Puglia: Train with transfers or rent a car for a leisurely drive?
4. Puglia Towns/Cities Exploration: Some on my list include Ostuni, Matera, Gioia del Colle (a must-visit to connect with family roots), Alberobello, Cisternino, Polignano a Mare, Monopoli, and Lecce. Considering the richness of options, I'm wondering how many of these are realistically doable. Any suggestions on which ones to prioritize or nix? Additionally, can you recommend the best central location to base ourselves for exploration, ensuring we can easily access day trips to these cities while also having some down time exploring the town we choose to stay in?
5. Nixing Amalfi Coast: Do we consider going straight from Rome to Puglia, and staying in or visiting a coastal town there for a similar beachy experience to Amalfi Coast? If we did this, perhaps extend our time in Rome?
6. Balancing "Off the Beaten Path": Does this itinerary feel too off the beaten path for a first-time visitor to Italy? Missing out on must-see places like Florence, Venice, Tuscany?

We appreciate any tips, feedback, or suggestions you can provide to make this honeymoon unforgettable for both of us!