I was there on the Monday after the week of All Saints Day, so the start of the "slow" season. I did that early morning tour and the guide said it's never really slow at the Vatican museums. The Sistine Chapel, when we cut back through to get to St. Peters was crowded with all seats taken, but not as packed as people say it is in summer. Expect crowds around the highlights (map corridor, Rafael rooms, Pieta in St. Peters, etc.), and then you won't be disappointed.
The bigger issue might be going to St. Peters after the museum if that's in your plans. Tours get to do the shortcut so don't have to go back through security. If you go to the museum and then the basilica without a tour, you'll have to leave the museum and then go through security again to get in to The guide pointed to the line and said it was about a 2 hour wait at 11 am. In November. If you planned on seeing both, you might consider going to one before lunch and the other later in the afternoon? More experienced travelers can give their opinion if it's an interest and you didn't want the tour.