As a parent, up front I would go for lessons but not buy shoes yet. I started out dancing in thick socks--comfortable and I could feel when I stepped on my partner's feet. (he danced in socks too)
If she loves it; shoes seem to be able to be gotten for around $100.
Our local teacher suggests campezio's jazz shoes for starting if you have them--the soft ones, not the tennis shoe looking ones. Over the years my daughter had every kind I think.
Dance training option vary widely depending on where you live. My son is going to school in Columbus Ohio, and there seemed to be quite a number of options for ballroom there; I commute to Houston regularly and found some interesting options there.
But I live in a small city 150 miles or more to the nearest larger city and here is what is available here:
there is a studio that used to do mostly ballet and tap but now offers some ballroom and women's exercise classes--nice people but I haven't their costs in front of me.
Where I go is an independent instructor I like: She charges $45-$50 for each session which lasts four weeks; monthly dances are $10 per person.
Specifically for Children: She offers a course that is fairly comprehensive for $135 which includes etiquette,manners, poise, as well as basics of ballroom dancing and the course ends with a dinner dance for the children.--this seems to not require any special shoes other than what you might wear to any formal dinner.
These are an example for a small city; if one were to travel from here to one of the large cities there are probably more options but also higher fees.
So, this is something of an answer.
