The pros of hiring a guide are that you get a lot of really good information and should be able to bypass the lines, though this is not always the case.
The cons of hiring a guide, you are tied to their schedule unless you are on a private tour, which can be very expensive.
The pros of going on your own with a good guide book and/or audio guides are that you can go at your own pace,if you schedule changes there won't be any penalties or money lost, you can see exactly what you want to see. It will save you a lot of money.
The cons of going on your own, you may not know where some of the sites are and thus, get lost getting there (which may not be a bad thing), You may not get as much information about the sites from a guide book as you would from a good guide.
You can tickets or book a tour of the vatican museums through the vatican website. This is the one place I tell first time visitors that they should get a tour. The museums are huge and a tour will take you to the most popular rooms.
Donna