The average score is 1000. Usually, best schools would have 1500+ scores as their median scores. Anything > 1400 would be median for many of the top schools. To Ta's point, do consult with your school counselor as different colleges have different expectations.
While SAT/ACT may be a requirement for most of the universities, there's no hard requirement for SAT scores, but most would have some guidance in regards to target score you should be shooting for (their median scores).