Remember that it's more than just the Sistine Chapel and Raphael masterpieces-though they are important. There's the Portrait Collection, decorative arts, Egyptian artifacts and much more. Even the rooms where the art pieces are displayed warrant a second look. There's so much to see that you'll have to narrow it all down and be strategic, otherwise you'll just be overwhelmed. If you are interested in the whole, plan for 2 half days. You could combine it with seeing St. Peter's or the Vatican Gardens.
There are two strategies that I have taken that were very different, but fulfilled my needs. The first was do some research on my own (I used an old art history book and the Eyewitness Guide) on a few of the famous pieces housed in the collections, plus plan to see the Sistine Chapel. By finding out where these pieces where ahead of time, I was able to go see them directly without wandering through countless rooms. The road to the Sistine Chapel is well marked and you could conceivably go to just see that. It's about a 20 minute walk straight from the entrance, so you could go there first, have it almost to yourself and then work your way back. In any case though, get there early. It opens at 9 am. Another good time to visit is around the lunch/siesta time 1-2 pm (less crowds). My second visit (and second strategy), which turned out to be much more satisfying, was to take a tour with an art historian (Liz from Scala Reale). Instead of just showing you pretty pieces of art, the art historian can put it in a context so that it's part of the history of the Vatican. They can also elaborate on the artist. Guides can navigate you through the crowds, take you into little known galleries and even show you things that aren't available for public viewing yet. At least Liz could. A good compromise between the two strategies is to take the Vatican's audio guide.
A tip: Bring a small mirror with you when visitng the Sistine Chapel. It will help you to see the ceiling frescoes (almost better than binoculars!) and save your neck.