I have been ballroom/swing dancing for around 5 years now. I love it. Talk about great exercise. It involves stength, balance, flexibility, and cardio capacity.
You do need some sensible dance shoes. Regular street shoes can cause injury, and dance shoes have special soles. I usually wear some modern dance flat shoes with a special padded cover for the ball of my foot. I used to do the high-heeled dance shoe thing, but it hurts. You can find them on line or ask at the dance studio.
See if you can find a local dance studio and sign up for some group classes. Most studios will have package deals for 4-6 week classes that are not too expensive. By doing this, you will get to see if you like dancing, meet some people, and get to see the teachers at the studio. After a short time, I started taking private lessons with a professional dancer. I picked things up so fast that group classes were boring to me....this way I could do what I wanted, when I wanted, and at my level. It's more expensive, but it was worth it to me.
I was always very sweaty at the end of our dance practice sessions. I would see other people looking so fresh, and I asked my teacher why we didn't look like that...he said BECAUSE WE DANCE, not talk.
I am not taking lessons right now; just can't afford it. I hope to start back one day. I miss it.