my girls do dancing. we didn't go when they were really little for various reasons involving one being clingy and them being close in age so they started at the same time age 4.5 and just turned 6.
They do an hour of ballet, an hour of modern theatre dance and half an hour of tap a week as well as a musical theatre/drama class. (I thought we would just do ballet but it seems to have escalated from there and they both want to add other styles too!)
I PERSONALLY think ballet is the base of most dance styles (with the exception of street and hip hop type stuff) and I know our dance school owner says the same, they have to do ballet there whatever combination of other styles they do. Ballet is obviously great for posture and coordination but it is also a lot more formal.
She might really like modern jazz (I have no idea how that differs from modern theatre to be honest but ISTD board do modern theatre and I think most of the other boards do modern jazz so they are probably just different names for the same thing)
Out of my girls friends they do a real mix, most do ballet or ballroom (a lot do ballroom, becoming very popular and some of them are amazingly good winning lots of competitions), a few do ballet, tap and modern, some do disco and quite a few do drama or musical theatre.
There are lots of different exam boards and different schools have very different approaches to it all. I THINK IDTA do a rosette or star scheme where they do a mix of different styles and take tests in each so they can try lots of different things but I could have misunderstood that.
Where in the country are you? I think you need to contact a few different schools and see what they offer.