St. Peter's Basilica and Sistine Chapel

One we have taken several times is the “Pristine Sistine” tour with Walks of Italy. 4 hours covers Vatican Museums, Sistine, and the Basilica.

Remember that the Sistine Chapel is within the Vatican Museums, so any tour that covers the Vatican Museums and St. Peter's (and there are many of these) will meet your needs.

I am in the process of planning our March trip to Rome

Dark Rome
Walks of Italy
Italy With Us

all offer Sistine Chapel and St Peter's Basilica combo tours

You can also find combo tours thru the Vatican's website

Yes. You want a Vatican Museum, Sistine Chapel and St. Peters tour. Just remember, silence is strictly enforced in the Sistine Chapel so your tour guide will brief you BEFORE entering and will not be providing any dialog whilst inside the chapel.

Last April I booked a tour directly thru the Vatican. Was a bit pricey, but worth every penny. Our guide was awesome, she spent 3 hours in the museums with us and left us at the entrance to St. Peters.

@work2travel: I would say silence in the Sistine Chapel is strongly called for, but very little enforced, except for the guide-tourist relationship you described very accurately.
When I was there about a year ago, the monitors continually called for "silencio" but the was a constant mulling of conversation from visitors who are just not to be bothered by rules.
There is also a prohibition on photography in the Sistine Chapel and in a past visit, I saw some people surreptitiously taking pictures with a phone camera.

Last year, there was not even such a pretense, as people were holding iPads up over their heads and snapping away, with no apparent reaction from the "silencio"-demanding monitors.