A gift for a debutante  

A great gift to give a debutante is a dress, provided you have some awareness of her tastes. As for dresses, it depends on the debutante's fashion sense. Some have no tolerance for clothes that are not designer and others are more tolerant of such things.

A book can be a good gift.

It all depends on when you plan to give the gift and how traditional the family is, but overall think of things that are classic and will be used a lot over time.