Advice to anyone about to take a trip is don't expect to remember all that you see in the Museums. Like many, you will get brain ache after being overloaded with so much visual stimulus and begin to overlook many interesting things. Each time something new will be seen with each visit made.
Some tips and advice -
Don't go early in the morning! It is best to have some lunch and go at around 2pm when there are no or less waiting. The Vatican Museums are now open from 8:30 am - 6:00 pm (last admission at 4:00 pm) which is much earlier and later than past years, the Vatican has done this to get rid of the lines that have been building up around their walls. Check the opening times at http://mv.vatican.va/3_EN/pages/z-Inf...
Note that the Vatican Museums are closed on a Sunday except the last Sunday of each month when entrance is also free.
Show respect and make sure your shoulders and knees are covered. There is absolutely no talking or even whispering in the Sistine Chapel. It is also the height of bad manners to take pictures of the ceiling, as the flash will contribute to the degradation of the artwork. The guards take their jobs very seriously and will escort you out if you fail to follow the rules. Also, note that, due to restaurations performed by a Japanese TV company that now has copyright on the ceiling of the Sistine Chapel, taking pictures is absolutely prohibited.
Take a tour through a reputable company; you will learn about what you are seeing which will end up being a more enjoyable experience. Tour groups allow you to go in the morning and skip the regular entrance line, but many times there are lines for the groups to enter... with the new enterance times this will not necessarily save you hours of standing in line and you will be paying more for the tour. On the internet or through your travel agent, you will find lots of options for tours of the Vatican, Sistine Chapel and St Peter's, as individual sites or combined with others.
Enjoy and don't forget to look at the floor, walls and ceiling and even out of the windows.