The documentary The Compleat Beatles is an excellent place to start.

There are many compilations spanning their career, of which I am partial to the ones known as the Red (1962-66) and Blue (1967-70) Albums. That will give you some sense of what you're in for.

Which albums are essential? Pretty much all of them. The ones that seem to be most well regarded are the ones in the middle - Revolver, Rubber Soul, Sgt Pepper and the "white album." But their early singles and late material on Abbey Road are also wonderful.

If you're ready to move on to solo albums start with Plastic Ono Band, Ram, All Things Must Pass and RINGO by John, Paul George and Ringo respectively.

Since I assume the show will revolve around their biggest hits, get the two Greatest Hits double album sets (the red one and the blue one), drop the needle, and you are on your way.

The Beatles invented, perfected or popularized just about every pop song-writing device, chord progression and harmony structure there is. Have fun!

I'd say the Love album would be best, since it should be exactly what you'll get to hear on the show

Love is a soundtrack remix album of music recorded by the Beatles, released in November 2006. It features music compiled and remixed as a mashup for the Cirque du Soleil show of the same name. The album was produced by George Martin and his son Giles Martin, who said, "What people will be hearing on the album is a new experience, a way of re-living the whole Beatles musical lifespan in a very condensed period."[1]

the red + blue compilation albums

there you'll find THE ABSOLUTELY VERY BEST of the Beatles; even if you don't feel like listening to their 11 studio albums (dozens of worthy album tracks), those two (now remastered) compilation albums are totally worthy / solid as gold

[Edited 9/26/14 4:33am]

Dancelot said:

I'd say the Love album would be best, since it should be exactly what you'll get to hear on the show

Love is a soundtrack remix album of music recorded by the Beatles, released in November 2006. It features music compiled and remixed as a mashup for the Cirque du Soleil show of the same name. The album was produced by George Martin and his son Giles Martin, who said, "What people will be hearing on the album is a new experience, a way of re-living the whole Beatles musical lifespan in a very condensed period."[1]

It's interesting but I wouldn;t necessarily start there if I never heard the Beatles before. Start with their records.