Any clothes that are suitable to wear to church are the proper styles to wear to a christening. The child's parents and godparents may want to dress up a little more for the occasion.
Women should wear conservative dresses or pantsuits to a christening. Since the ceremony is often in a church or other religious venue, it is not appropriate to wear anything that shows too much skin, such as a strapless dress, a top that shows cleavage or a very short skirt. Men should wear a sports coat or a suit and tie. If the weather is particularly hot, men can often wear just a dress shirt and tie.