The "correct" number is 18 (or multiples of it) and is based on the word chai, life in Hebrew.
A Bat Mitzvah is in no way a "mini wedding", though the festivities are often quite elaborate. The service itself is the focus of the day, and represents the childs symbolic transition to adulthood in our religion. The party, after the service, is a celebration of their reaching the point where they can participate in an adult fashion in their religious life...reading the Torah from the bema (leading the service), be counted as a member of a minyan and things like that. The equivalent service for boys is called a Bar Mitzvah (son of the book). Only Reform and Conservative Jewish groups acknowledge a Bat Mitzvah, Orthodox still do not allow their girls this rite of passage.
It is a stressful, though exciting time for these children. They are required to learn and understand (and chant) whatever portion of the Torah is to be read on the day of their Bar/Bat Mitzvah as well as the prayers said on the bema during services, and to write a speech about their "portion". Most temples expect them to work on this a minumum of once a week with a tutor or clergy for approximately six months prior to their simcha, as well as to continue their regular attendance at Religious School.
Hope this was helpful to you.