In contrast to social dancing competitive dancing requires different kinds of shoes depending on the style you are competing in. International Standard and American Smooth styles both require close toed shoes while American Rhythm and International Latin require open toed shoes. Heel heights vary depending on what you're most comfortable in but can range anywhere from half an inch high to 3" tall.
There are so many options as to what you can wear on the competition floor. From long gowns covered in Swarovski crystals to full suits with a tailcoat there is a wide range of outfits you can step out on to the floor with. Depending on the style you are dancing and whether you are a lead or follow will determine what you would wear. Your instructor can help you pick what best suits you.
There are four styles you can compete in which are International Standard, American Smooth, International Latin and American Rhythm. Depending on your dance experience or what you're most interested in your instructor can suggest one or more styles to compete in. Many people compete in more than one style!