As I have stressed many times before, ballet, ballet and, oh yes, ballet.
Every other dance style passes through ballet, and that is the basic technical background you need. It all comes from ballet.
Ballet also teaches body awareness and discipline.
Barre work can be boring as all get out and at the beginning, can leave you with muscle spasms at inconvenient times like the middle of the night when you are sound asleep, but you learn so much that has nothing to do directly with dance like body carriage/posture and concentration. It is also a great workout.
Ballet.
Some dance-heavy shows will put you through paces first. Some shows are not that dance-heavy and you sing first. South Pacific to name one, A Little Night Music for another.
"If my life weren't funny, it would just be true. And that would be unacceptable."
--Carrie Fisher