I didn't watch live many of them because of the prices for tickets (they're really high!) but I can say that I'm a small fan of their shows. I think that Broadway musicals are the best in case of plot, decorations and singing (and the ones I watched prove this) so nothing strange that they became so popular
Which genres in this case do you prefer? From the ones I watched, I can recommend you
Chicago, it's a good detective story about celebrities and their criminals (not worse than the movie I might say).
Wicked is a very popular musical now, it's an original thing for those who like stories about magic and especially famous
The Wizard Of Oz, it has an interesting plot with the deep meaning.
Hamilton is a totally historic thing, it's main feature and uniqueness is in its hip-hop musical numbers, if you like both history and r'n'b music, you should really watch it (personally I liked it very much after watching live), besides like it's seen from this
link it'll be on stage till the end of the next year
I didn't watch
The Book of Mormon, however I saw in many reviews that it's a good comedy. The same is about
Cats and
Miss Saigon.
Hope this was helpful for you!
