Ballet is a great way to stay in shape and have fun. Most dance studios offer adult classes at beginner and intermediate/advanced levels. Whether you have a child in dance or you are just looking for a fun exercise class, ballet can be an awesome choice.
Don't let the fear of looking weird in a leotard keep you from signing up for class. Usually leotards are not required. If you are new to dance and don't own any dancewear, simply wear tight fitting exercise clothes like leggings or yoga pants (think lululemon's tight fit) and a top that fits close to the body. You will probably be jumping and doing some aerobic movements, so wear a sports bra if you feel you need the support. Male dancers can wear a close fitting t-shirt (avoid shirts with big logos or pictures) and sweat pants or long athletic shorts. If you don't have ballet shoes, wear thin athletic socks to your first class. Most teachers are ok with this as long as you get some ballet shoes for subsequent classes.
If you want to get some dancewear, I recommend choosing styles that are modest and comfortable. Tank, short sleeve, and long sleeve leotards come in various styles that look nice and can hide a bra if you feel like you want to wear one. Black footless tights or ankle-length black leggings are more opaque than the pink tights most younger students wear, so they can make you feel more covered. A dance skirt (wrap or pull-on, above the knee length) or a pair of warm-up shorts can round out your look and provide some extra coverage. Male dancers can look into getting jazz pants, tights or leggings, and dance shirts, but any exercise wear will always be appropriate for class as well.
When you get ballet shoes, first consider whether or not you want to wear them with tights. If you prefer footed tights or wearing your convertible tights "down" over your feet, get shoes in the same color as your tights (black shoes with black tights, etc.). Especially if you wear black footed or convertible tights, do not get pink or nude shoes. It does not look good. If you wear footless tights, choose ballet shoes in any color you like.
The most important thing about ballet shoes is the fit. For an adult, I recommend choosing split sole ballet shoes in leather or canvas. Avoid imitation leather if possible. Leather and canvas stretch and mold to the foot after some wear, so you need to have shoes that are snug to the foot. Workers at your local dancewear store can help you find a good fit. Make sure the shoe does not gap at the sides and there is not extra room at the toe of the shoe. The shape of your big toe should be visible through the material, and you should feel the end of the shoe with the tip of your toe (but it should not "squish" your toes or hurt). This may be tighter than you are used to, but it will really help you dance your best.