I just had a client come from China to put her child into Irvine schools. If you rent or buy, you are establishing residency and the school district asks for proof that you live in the school boundaries. The question about a VISA and green cards....I would recommend a call to an immigration attorney or your local US consulate where you live to make sure that you do things necessary to enter and move to the US.
The story of all immigrant families here in Southern California! GOOD LUCK!!!