A few suggestions….
1900: George Washington, Jr.
As far as I know there is no recording. Several people have suggested WIZARD OF OZ, a very good choice except its score was a mish-mash by a variety of composers tailored to the talents in each production. BABES IN TOYLAND has a full score by Victor Herbert and can introduce the early operettas by him as well (RED MILL, NAUGHTY MARIETTA) as prime examples of the genre.
1910: Watch Your Step
-Same problem with no recordings. Try IRENE (the decade's biggest hit)
1920: Show Boat
-No question. But if you want an example of the 20’s musical comedy either NO NO NANETTE or GOOD NEWS would work
1930: Porgy and Bess
-Again, no question unless this is considered an opera. For 30’s musical comedy, ANYTHING GOES is probably the decades top choice. OF THEE I SING
1940: Oklahoma
-Excellent! The biggest hit of the decade.
1950: West Side Story
-Not the decade’s biggest hit (MY FAIR LADY was) but probably in terms of what followed the most important show.
1960: Fiddler on the Roof
-While it was the decade’s biggest hot, CABARET probably had more impact
-1970: A Chorus Line
-Again it was the decade’s biggest hit but COMPANY and SWEENEY TODD are probably the most important works
1980: Cats
-No. It’s a good example of spinning candyfloss but a very poor example of theatre writing. For an example of a British megamusical I’d opt for LES MISERABLES. SUNDY IN THE PARK was the Pulitzer prize winner, though as you mentioned INTO THE WOODS is more accessible.
1990: The Lion King
- I would not choose this as the decade’s best or even most representational show. RAENT (another PP winner) or RAGTIME would be more appropriate.
2000s:
-The decade has not been strong nut THE PRODUCERS is probably the last word in traditional musical comedy. WICKED is the decade’s biggest hit, and LIGHT IN THE PIAZZA the chamber opera.
A good guide would probably be the PBS 6-hour history of Broadway musicals. It doesn't cover the early operettas but covers just about everything else.
Cast albums are NOT "soundtracks."
Live theatre does not use a "soundtrack." If it did, it wouldn't be live theatre!
I host a weekly one-hour radio program featuring cast album selections as well as songs by cabaret, jazz and theatre artists. The program, FRONT ROW CENTRE is heard Sundays 9 to 10 am and also Saturdays from 8 to 9 am (eastern times) on www.proudfm.com