My sister and her husband attended Rice so I am very familiar with the quality of education available at Rice. Since your parents and brother have attended Rice I will not provide info on Rice but help you understand how you could fit in at Princeton.
“My Mom is particularly scared about Princeton being elitist and full of privilege that wouldn’t necessarily be found at Duke or Rice.”
This is not a problem. I attended a public HS as did most of my friends. 60% of the students receive financial aid. There are more first gen low income students than alumni children. Visit for Princeton Preview and you will discover the other admitted students are similar to you.
The residential college system at Rice and Princeton are similar; however, I believe Rice has changed since my sister attended.
Frats/sororities are not important at Princeton. For their junior and senior years students have the option to continue to eat in their residential college or join an eating club. Students that want to join an eating club may join a club simply by telling the club that they want to join or go through a “rush” type process to join other clubs. If you join the Princeton University Orchestra you might to decide to join the same eating club as your friends in the orchestra.
Both the Rice and Princeton orchestras are considered among the top 20 in the US. Other instrumental groups at Princeton are Princeton University Sinfonia, Princeton University Wind Ensemble, Cornel West Theory, Shape Machine, Princeton University Chamber Ensemble, Undergraduate Composers Collective, Music in Mind, Princeton Classical Music Players, Princeton Pops, and many brass and international groups. You may be interested in the Princeton Laptop Orchestra. https://www.youtube.com/channel/UChiK8wRwAugDuABbtHmNK4g
When you attend Princeton Preview you may want to obtain information on the program with the Royal College of Music, London were exceptionally talented students may qualify for a five-year, double-degree program (Bachelor of Arts from Princeton and Master of Music from the Royal College of Music) that includes study in London for the fall term of the junior year. Visit the Lewis Center for the Arts. This complex has many practice rooms and performance space. The residential colleges sponsor trips into NYC or Philadelphia to listen to concerts, attend Broadway plays, or attend an opera.
Princeton’s music department was established in 1946, and 15 years later it became one of the first in the country to offer a Ph.D. in composition. Former Professor Milton Babbitt helped to establish and co-directed the Columbia-Princeton Electronic Music Center in New York City, which housed the RCA Mark II Electronic Music Synthesizer, the first American machine designed for the production of electronic music. The Certificate Program in Musical Performance provides an opportunity for students to develop their performing skills. Students in the Program in Musical Performance are required to pursue some kind of performance study and therefore the department subsidizes the entire cost of weekly lessons taken with teachers under contract with the department. Caroline Shaw GS, who studied composition in the University’s Department of Music, has won the 2013 Pulitzer Prize for Music for her a cappella piece Partita for 8 Voices. Shaw is the youngest winner of the Pulitzer Prize for Music since the award’s inception in 1943. Julia Wolfe *12 is a 2016 MacArthur Fellow. She is a post-minimalist composer whose work combines influences from folk, classical, and rock music. Her pieces, including Cruel Sister (2004) and Anthracite Fields (2013) which was awarded the Pulitzer Prize for Music in 2015. Pascal Le Boeuf GS composition Alkaline was nominated for a Grammy in 2017.
Since you enjoy math you may be interested in the research by Professor Dmitri Tymoczko, a Rhodes Scholar is a composer and music theorist. In the first paper on music theory published by Science magazine Dmitri showed that two-note cords occupy the space of a Mobius strip, a two surface embedded in a three-dimensional space. More complex cords inhabited a multidimensional space that is twisted back on itself called orbifolds. Music cords have a geometric shape.
http://www.princeton.edu/pr/pwb/08/0428/music/ and http://www.sciencenews.org/view/generic/id/9450/title/The_Geometry_of_Music and his YouTube video: http://www.youtube.com/watch?v=NnvynOyZI-Q
While I would expect that ME at Rice and Princeton would be similar; however USN&WR does rate Princeton higher.
Enjoy Princeton Preview.