How have the vatican lines been since high season started? I have heard that it has not been neccessary to buy tickets in advance as the lines have been short and at times non existant.
We visited the Vatican Museum mid-June on a Vatican tour around 12:00. Lines were long earlier in the morning, but no line in the afternoon. A few of the tour guides who were outside the museum were asking each other what happened to the busy Mondays they usually see. I would probably err on the side of buying in advance though, unless your schedule is very flexible and you try the afternoon.
I just went to the Vatican museums/sistine chapel/st. Peter's a few weeks ago and it was VERY BUSY. I would definitely suggest going in the morning if you can. We did an afternoon tour (through Viator) and by the time we got into the Sistine Chapel there was what seemed like 1000 people in there. It kind of ruined it for us.
As well, try to go on a Wednesday morning for a chance to see the Pope! We missed it by a few hours, which is too bad :-(
We just visited the Vatican on the 9th and I am SOOO glad that I prebooked! The lines were forever long.