Into the Woods, it's really funny, the plot is deep and brilliant and it's a tearjerker if you're a parent. It's by Sondheim, they guy who did Sweeney Todd. I personally love Into the Woods, but the music isn't...I guess what I would call tradition Broadway. It was put on DVD a while ago, but originally came out in 1989, I believe? Plus, Bernadette Peters.
Rent is another favourite. It has a great plotline, and the backstory about Johnathan Larson just gives it more heart than it has. Though if you have a problem with homosexuality, I wouldn't recommend it. But still, if you're looking for music, I definitely recommend Rent.
My Fair Lady, excellent musical, but it is older. I love the music and the story, because it is designed like older movies and musicals.
The King and I, positively phenomenal, it is rather long, but it's Rogers and Hammerstein. It's truly amazing, and again made with care like an older movie. It is one of my favourites ever. I strongly recommend it.
West Side Story, another older one, but another Sondheim. Romeo and Juliet story with songs you've heard a million times. It's very amazing, and the choreography is great.
If you like choreography, go for Cats as well. It's a little odd, but the choreography is just brilliant, the dancers are so talented, and the song Memory is always a favourite, if not overdone.
If you haven't already, The Sound of Music is a great movie, for any age. Julie Andrews is talented and stunning as always, and it is a classic.
I almost forgot Chicago. Completely amazing film. I love it and it deserves all its praise. Plus, it's satyrical song "We Both Reached For the Gun" is phenomenal. Cell Block Tango is great. The music, filming and everything is flawless.
There are a ton more I'd recommend as well, Oklahoma, Fiddler on the Roof, 1776, Victor/Victoria.
There are a million great musicals out there on DVD, just need to search a bit, hope I helped.