As I'm sure most are aware, Vatican City is a country in its own right, after being ceded to the Catholic Church in 1929 through the Lateran Treaty. The Vatican however has been in existence in some form or other since the return of the popes in 1377, with the majority of the city being built in the 1500's.
The city is split into 3 key areas that are accessible to tourist, and a number of others that are private, such as the gardens and the palace. Of the 3 tourist areas, 2 (the Vatican museum and the Sistine chapel) are accessed and ticketed via the same entrance, whereas St Peter's Basilica is free to the public, but cannot be accessed from the Sistine chapel without a guide.
In our opinion, unless you are overly into your religious art and sculptures, the museum and Sistine Chapel are probably not worth it for the cost (especially with the cost of the queue jump). The Sistine Chapel is a great accomplishment, but the awe is ruined by the fact that you're herded in like cattle.
What we'd recommend is skipping the ticketed bit and just doing St Peter's and the tomb. Get there early enough and you'll avoid the queues, it's free in, and the church is simply breathtaking. Also you get to admire St Peter's Square while you wait!
Best time: Go early in the morning to avoid the queues.
Top tip: Skip the museum and the Sistine chapel and head straight to St Peters.