Sarah Mahnke-Baum, Arthur Register and Julian Brastow became friends at their neighborhood preschool in San Francisco's Cole Valley. But as they march off to elementary school this week, they'll find themselves heading in very different directions. Sarah, the daughter of a public school teacher, will attend kindergarten at a prestigious all-girls private school tucked between Sea Cliff and the Presidio with an annual tuition of $19,000. Arthur, whose family isn't Catholic, will attend second grade at a Catholic school in the Richmond District for $4,500 a year. And Julian will be a first-grader at the free public school just around...