This is beginning to change somewhat in the US as policymakers recognize that not all property taxes are generate the same amount of revenue for schools.  Some states (including Wisconsin) are beginning to use other state revenue sources to try to equalize this funding.

The federal government has traditionally been more involved in higher education through all of these mechanisms.

(A) school choice is incorrect.  School choice basically allows a parent to send their child to a school (typically public) outside of the traditional school boundary area.  Both of these, though, are attempts to introduce competition into the school systems.

The courts have ruled that public funds can be used for secular (nonreligious) purposes even in a parochial school.  For example, money could be used to buy math or english texts, but not to buy bibles.  A current controversy surrounds whether school vouchers can be used to send children to parochial schools.  Wisconsin may be a test case where its state Supreme Court has ruled it as constitutional.  The federal Supreme Court may hear this case in the future.