Karen,
The lines to buy tickets for the entrance to Vatican museums can be extremly long. When we went to Rome last year our italian Limo driver suggested that we go at lunch time. This seemed counterintuitive to us since most people suggest to go first thing in the AM( although then they'll tell you they had to wait in line for 45min to over an hour!).
We followed our driver's advice , arrived around 1PM and there was NOBODY in front of us to buy tickets. That was unbelievable as we had driven twice by the Vatican on prior days in the AM on our way to other places and the line snaked all the way around to Saint Peters!
In the Vatican museums also allow time for the Raphael stanzas( rooms) with his magnificent mural paintings. These are on the way to the Sistine chapel. As mentioned before, everything is on the way to the Sistine chapel.
In St. Peter's basilica don't miss when you walk in, on your right, the beautiful sculpture of the Pietá , by Michelangelo( my favorite, even more than his David). It has a glass panel in front of it because years ago a maniac hit it with a hammer!! Thankfully the damage wasn't major and they were able to repair it.