If medical school is something you're interested in (I think this is a safe assumption), I would choose Rice-Baylor's BSMD program.
The reason is that many pre-med students (whether they will admit it or not) took a watered-down course load and chose easy majors so that they could maintain a high GPA, study for the MCAT, and do a bunch of bullshit to impress medical schools. In a lot of ways, that ruined their college experience. Always wondering how things you do will affect med school admissions is a terrible way to go through college. It narrows your options and is the opposite of freedom.
Now let's say that you choose Rice-Baylor instead. You don't have to optimize for med school admissions because you're already in. Now you can take hard classes and do any major without fear of having a competitive GPA for med school. You can do internships that have nothing to do with medicine. Basically, you can do all the things a pre-med student (or you at Columbia) would not do.
This is the freedom option. It's the option I would choose if I were in your position. Also Rice and Baylor are great schools. You can't lose here.
With your freedom, spend your summers in Silicon Valley. If you got into BSMD I assume you're pretty smart. It will not be hard to convince people to hire you.
I know this is a big decision, if you want to chat more, email me at gordonmzhu[at]gmail[dot]com.