7. Oklahoma (very important as it's considered by most to be the first book musical) Except that it ISN'T. All musical comedies and operettas had books. If you mean integrated with the songs SHOW BOAT did that 16 years earlier and even that was not the first. Because of its historic importance and long-term popularity, OKLAHOMA! is often incorrectly credited with innovations.
It was Broadway's first musical to play over 2,000 performances, and it was a show that gained attention far beyond the New York theatre-goers.
It was NOT the first show to have an "original cast recording": Decca had alredy recorded PORGY AND BESS and THIS IS THE ARMY. (OKLAHOMA! was the first OCR to sell over a million copies.)
It was also, NOT the first show to use ballet. (ON YOUR TOES did that in 1936.)
But it is an important show and one that still works for audiences despite its simplistic story.
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