I have a question: at what point do kids go though catechism? If I convert, are my kids included? (Actually, my last one needs to be baptized--we have never had a church community we called home long enough to get him dunked.)
Every church is different regarding how catechesis is done. Many churches have inquirer's classes that cover the basics and the most common questions that people have. In smaller parishes, you might just meet individually with the priest to discuss questions and what you've been reading. The priest will tell you what he recommends regarding your children. Most of the time, just attending the services is enough. Most priests will have a certain length of time that they want you to attend before they will take formal steps toward discussing reception into the church -- very commonly, they will want you to have at least one Lenten/Paschal season under your belt.
In the Orthodox Church, our children are baptized and immediately chrismated (confirmed), and begin to take communion from that moment on. There is no process of step-wise progression through the Church -- first communion, confirmation, etc... They are full communicating members from minute one.
Many churches have Sunday Schools with educational programs to teach elements of the faith that will not be obvious from the services themselves to a child. Some are good, others are a waste of time. In the "old countries," this education was often integrated into the public school system, so the Orthodox Churches in the "diaspora" are still figuring out how to accomplish the same thing here. Right now, it is considered to be primarily a family responsibility to educate one's children in the faith.