When you're checking out studios, be sure you find out early what their regular price for lessons is. Some studios, mostly chains like Arthur Murray but also some independents, sell their lessons only in packages including both privates and group classes and they can get expensive fast. If you don't have a lot of money to invest in learning to dance, look for a studio where you can go "a la carte," paying just for what you want to take.
For shoes, if you get serious about ballroom dancing, you will want to get dance shoes with suede soles, as they move best on the floor, but you can start out with any pair of secure, comfortable shoes. Avoid sneakers or rubber soled shoes, as they stick to the floor too much.
Welcome to dancing! You'll love it!