Here are some things you perhaps ought to see, grouped by composer. I have tried to avoid just picking my favourites and also to give a good balance of styles and eras.
It's worth noting that this is something I have just cobbled together (I will asked Shelley and Tracy to have a look and add anything that they think I have missed) and you should be investigating other things as well.
There are film versions of many of these - very often these will differ significantly from the stage version and it may be worth watching both!
Leonard Bernstein
West Side Story
Candide
Cole Porter
Kiss me, Kate
Anything goes
High Society
Rodgers and Hammerstein:
The Sound of Music
Oklahoma
South Pacific
Carousel
Stephen Sondheim
Company
A little night music
Into the woods
Sweeney Todd
Andrew Lloyd Webber
Evita
Cats
The Phantom of the Opera
Kander and Ebb
Chicago
Cabaret
Lerner and Loewe
My Fair Lady
Jerry Bock
Fiddler on the Roof
Marvin Hamlisch
A Chorus Line
Jason Robert Brown
Parade
The last five years
