In this order: jazz, ballet, modern. Modern is a distant third. Jazz is the movement language of musical theater.
But don't just take my word for it. Try asking your questions at any of the following sites: www.danceart.com, www.balletalert.com, www.criticaldance.com. The dancers and former dancers who run these sites and post to them will be more than happy to assist you.
There's also a magazine, Dance Spirit, that you could check out. It probably has a website, too.
-S-[/i]