Kathleen
I just realized that your "ancient Rome" day is on your arrival day. I would say to visit what you have the energy for - being outside is good for combatting jet lag. Then, the next day, so the rest.
I agree on the National Museum of Rome. We visited it on a previous trip to Rome, but primarily because I love mosaics, and they have a lot of them. I would always choose Galleria Borghese over the National Museum.
Visit the Pantheon whenever you visit Piazza Navona and that area. All of them are also good to visit at night, but you can't go inside the Pantheon at night.
If you've been reading Rick Steves, you know that reservations are required for the Galleria Borghese. On our recent trip, while we knew what to do because we've been there before, I thought it would be confusing to someone who was visiting for the first time. First, you go to the basement to collect your pre-reserved and prepaid tickets. Often there's a line for the ticket pickup (or, if you're late, like us, there is no line anymore!). Then you move over and check all your bags - only the smallest bags are allowed. Then you go outside, and up the big stairs to the entrance to the museum. As we entered, what looked like maybe a group from a cruise ship, that already had tickets, tried to get in without checking bags - about 80% of them were turned away (not very nicely, BTW) and sent to check their bags.