As a side note, there is a shortcut from the Sistine Chapel into the
Basilica which RS describes in his tour book, and for us it worked
beautifully and saved at least 90 minutes of walking/standing in line.
That shortcut is technically reserved for tours. While some RS posters where able to get through without difficulty, other independent tourists have reported being denied access by the guards. It's sort of up to temperament of whomever happens to be stationed there, and should not be considered a fool-proof, time-saving route to the basilica unless you're with a tour.
gargbi, due to the crowds and general sensory overload of the museums' vast holdings, about 3 hours is about all but the most dedicated museum lovers can manage, even just hitting the highlights. You will be good and tired at the end of it! You'll also be able to remain in the basilica for as long as you wish to when your tour is over. I don't know as they cover the crypt - which is accessible to all without a separate tour or reservation - so you could do that on your own. This is NOT the scavi - or necropolis - at the deeper level which does require a tour and reservations well in advance.
People speak highly of Walks Of Italy's "Pristine Sistine" tour ( and some others) which allow early access to the Sistine before it's completely mobbed. It's pricey, though, so you might consider the Vatican's own early-entry offering with breakfast for quite a lot less? It's not a guided tour, although you are given an audioguide, so you can spend as long in the museums as you wish to. You will not be able to chance exiting into the basilica via the shortcut as, as far as I know, the audioguide must be returned near the front of the museums.
http://www.museivaticani.va/content/museivaticani/en/visita-i-musei/scegli-la-visita/musei-e-collezioni/colazione-ai-musei-vaticani.html
There is also the version with a human guide.