Advice on selecting a major/college type!

With wealthy parents who cannot or will not pay much for your college costs, your options will be limited, like for many college students.

Please lose the anti-public-school attitude, since that will needlessly limit your options.

If you do have a 4.0 GPA and high test scores, investigate merit scholarships:
http://automaticfulltuition.yolasite.com/
http://competitivefulltuition.yolasite.com/
http://nmfscholarships.yolasite.com/ (if National Merit)