This evening, we went to see Mallika Sarabhai dancing Kuchipudi at Bozar. Kuchipudi is a dance from South India. It looks a little bit like Bharatanatyam (with my non-specialists eyes) but with more contact with the audience (or is it the way it was performed by these specific dancers?).
I think that if you want to see only one dance from India, you have to see Bharata Natyam. If you want a gentle introduction to Indian dance, Kuchipudi can be more accessible.