I guess my advice depends on if you have kids, and how well you recover from jet lag. Regardless, I would not try to do too much that first day. The days in Rome are filled with walking, and if you are going in the summer, it will be hot and crowded. It is amazing how much energy it takes to maneuver through crowds on a walking tour. Disney was brilliant in planning the relaxing time in Tuscany after Rome, you will need and appreciate it.
If you don't have kids, and the Vatican is important to you, you may want to try and go there. On the tour you only see a smidgen of the art on the way to the Sistene chapel.
If you are there in July, as we were, the entire country is having clearance sales before the traditional month long August holiday that many Italians take. If shopping is a priority you could do that your first day.
I recommend getting a good guide book (Rick Steves or Frommers) and narrowing down your options that are most appealing.
You will have a wonderful trip.
