When a student in China finishes the equivalent of US High School,
what is his or her options concerning education. Are there just
universities? Are there trade schools? Are there for profit
educational schools in existence? If so, are these for profit schools
China based or from the US, UK, India etc.

Looking for links, and summaries. Not necessary to answer all
questions for complete answer. Looking for good web starting points.

http://www.moe.edu.cn/english/index.htm

You can have a look at it.