Engineering & Management at Princeton
Congratulations on your hard work so that you are in a enviable position to make a choice.
You did not mention which engineering program you are interested in; however you will find that the Princeton engineering program is one of the best in the country. There are multiple ways of combining a engineering education with management preparation.
The economics department is one of the best in the world. The Operation Research and Financial Engineering major is a great preparation for Wall Street or consulting. A certificate program in Finance will provide the background to become a CFO. Also consider the Engineering and Management Systems certificate program.
With a little research you can easily develop a M&T type program at Princeton. When you visit the campus you will see you can obtain the education that you desire.
Most of the best business schools do not want students from a business undergraduate background. Major in engineering, take interesting courses in economics, finance, OR, entrepreneurship and go to a top business school for an MBA.