The Rebbe's guidance to parents choosing a school or yeshiva:
Yiras Shamayim comes first. In choosing a school, the first consideration is the level of yiras Shamayim and a Torah-true education, even if this means less cultural familiarity; choose an environment with high standards if you want your children to grow in them (IK 4205, 7610). Choose the best possible education without hesitation (IK 1669). Chabad schools are under the guidance of the Rebbeim (IK 4365), and the Rebbe strongly urged enrolling children in them where possible (IK 6837). A son who has begun learning Chassidus should not continue in a yeshiva where it isn't studied (IK 2126).
Public school is not the answer. The Rebbe stated unequivocally that public school is not an option for a Jewish child's education (IK 10359). Limiting secular studies and increasing Torah learning strengthens children both spiritually and physically (IK 2268). Even where only a few hours are possible, send children to a religious Talmud Torah for daily contact with Torah and with observant friends (IK 1710).
Match the school to the child. Choose an environment that suits the child's own good qualities, and beware of places whose influence could undo them (IK 10377). In choosing a yeshiva for an older son, look for one that fosters yiras Shamayim and growth, not just prestige, and one devoted fully to Torah study (IK 4497, 5158, 6067).
Don't take a child out of yeshiva for financial or health reasons. Don't remove a son from yeshiva to teach him a trade (IK 3614), nor for the sake of fresh air — true health comes from an environment of yiras Shamayim (IK 3214). Where a child has difficulties, address them locally with care rather than sending him away (IK 8107, 8125).
See also: Parenting – Your child's friends and surroundings; Livelihood – Torah study vs. going to work.