In 2017 I did this Dark Rome Express Sistine Chapel, St. Peter's Basilica and Vatican Crypt Tour. Others with our group went to the museums after the Sistine. This company has lots of tour offerings, and I'll never go again unless it's at a time when crowds are very small.
It was my 3rd visit. The first time the Sistine hadn't been cleaned yet, but none of the options were crowded (1977).
The 2nd time (2009) it was a guided tour, but later in the day. The Sistine was clean, crowded and noisy, complete with the din the guards tried to keep down, but only made worse. And the cattle-through-the-chute crowding in the museums was miserable. I felt sorry for the short people and little kids who could only see backs and butts, respectively.
The 3rd visit was early enough that we could be in the Sistine with only about 100 people instead of the usual thousands. BTW, that is not an exaggeration. We were able to sit and take it all in and although some people were talking, they were very quiet and respectful.
St. Peter's is always impressive, but I loved being there so early that they were cleaning the floors with a zamboni-like machine and people also were quiet and respectful.
Seeing the crypt was very moving to me, because I got to see the tomb of Pope Paul VI. He was the Pope who did the Christmas Eve Mass I attended in 1977. He was very frail then. I'm not Catholic, but as he was carried through the center aisle from the back of the Basilica to the front, he looked me straight in the eyes and made the sign of the cross. I will never forget that.
I think the Vatican museums are amazing, but they are huge. Even if you get in very early, like most large art collections, they are exhausting to visit because of the visual overload, not to mention that I don't remember a single place to sit and really look at anything. It has been 10 years, so maybe that's changed. The collection is definitely worth seeing, but do try to go very early so you'll be rested and ready for some significant visual input.