The best answer of all is “pure pleasure” for high school language choices. First, because it’s one of the few subjects in which students have the luxury of choice, and second, because you’ll do better learning a language you enjoy. I would regard any language learned in high school to be the first language learned in a lifetime, not the only foreign language learned. By the way, if you know your school already, there’s no harm in contacting current parents or students to ask about the relative strengths of the different departments.
It pays to be realistic about your child’s chances to do very well in languages, especially when it’s a language with many heritage speakers. http://media.collegeboard.com/digitalServices/pdf/research/2014/STUDENT-SCORE-DISTRIBUTIONS-2014.pdf
More than 10,000 students took the AP Chinese exam last year. More than 7,000 earned a 5. Of those who were not heritage speakers, though (“standard group”), only 455 earned a 5.
In Latin, there are no heritage speakers. Only 866 earned a 5. That was 866/6,542 = 13.2%.
Academic boarding schools teach the classics very well. If your child manages to take Latin and Greek, he or she can earn a Classics diploma at certain schools.