Probably the most important thing you can wear is a pair of comfortable shoes. Contra dancing can be quite vigorous. You will need to wear shoes that allow you to move freely and safely. Leave the high heels at home, opting for low or no heels. Choose a shoe with soft, smooth soles, as hard soles may cause damage to wooden dance floors. Rubber soles are most comfortable, but make sure they aren't too thick...thick, rubber-soled shoes might stick to the floor during turns and twirls, causing potential injuries to knees and ankles. Use common sense...strappy, open-toed sandals might look sexy, but you'll feel much more at ease in comfortable, sensible shoes.
As for clothing, casual dress is best. Loose, comfortable clothes that don't restrict movement will feel and look the best. Some women enjoy wearing skirts or dresses that twirl when they turn or spin. As for men, light slacks or shirts with t-shirts or lightweight dress shirts are popular choices. Some men like to dance in skirts, for the same reasons as women. Don't worry too much about your appearance, though...contra dances are meant to be relaxing, stress-free events. Save the fashion for the nightclubs.