When I visit Vatican, it was a free day.

Vatican Museums free on last Sunday of the month! ( Museum lead to Sistine Chapel, I don't know you can just visit Sistine Chapel )

The entrance is to the north side of city, free or not free day, always long line.

Museum/Sistine Chapel is one long line; St. Peter's is another long line; if you visit top of the dome add a third long line.