My husband and I just returned from our 3rd trip to Italy. The first time, we hit the "big" 3- Venice, Florence and Rome. The second trip was spent exploring the Amalfi Coast and Pompei, the third trip we visted Lake Como, the Cinque Terre and Milan. In my humble opinion, I feel on your first trip to Italy it would be a good idea to see the "big" stuff. Being a fan of history, you will be blown away by the historical sights, museums, churches, etc found in the larger cities. Trust me, being in relatively good shape will be greatly appreciated when you're climbing to the top of the Duomo or wandering around any city. You will walk and climb til your calves are aching! If Rome and Venice are your definites, and you're not sold on Florence, just look on a map, there will be plenty of other cities along the way that would be worth stopping in. (Siena, Lucca, Bologna). The CT would be a bit of a detour, and again, it will depend on the amount of time you have to decide if it will be worth it.
I feel we were able to relax more on our subsequent trips, knowing that we had seen all of the major sights. If you feel like this might be your one and only trip to Italy, then some place with wonderful scenery, but not too much of a detour would be a good idea (maybe Verona and Lake Garda). Again, just my opinion. Happy planning!!!