Is the number of candles one lights for Shabbat based on halacha or minhag? I have been in homes where there are three candles lit and in other homes where the number of candles lit corresponds to the number of family members.

The basic mitzva requires that at least one candle be lit (MIshna Berura 263 22). It is accepted, however, that no less than two be lit (see Shulchab Aruch 263 1). Some homes light according to the number of children, some light seven, others ten (Mishna Berura 263 6; Halichot Beita 14 18). The R'ma writes that a woman who forgot to light candles one shabbat adds a third candle from then on (and if she forgets to light more than once, one for each shabbat that she forgets; Mishna Berura 263 7).