As a parent of two teenagers in public magnet HS (one of which is top 10 in the US) I still say homeschooling is by far the best and what my wife and I would have done if it was an option.

Home school is best, private school if you can, public school if you must.

Its a weird stereotype of home education that people with no, or limited, experience have of it. It is far better preparation for the "real world" than schools are.