My daughter graduated from Rice in BIoengineering. The department is fantastic. It’s relatively small and their faculty is super engaged and student-focused. When my daughter applied to grad school she had very strong letters of recommendation because she had gotten to know her professors very well. Their classes are very project focused so you are applying the information you’re learning and end up with some really great design experience to talk about in interviews. My daughter worked on a project she enjoyed so she continues working on it independly for credtit the following year. A professor oversaw what she was doing and she was able to connect with other staff and grad students for help in areas where she needed it (for instance electrical stuff and come programming). They also have some great minors that mesh well with Bioengineering. The two most popular are probably Engineering Design and Global Health Technologies. Their graduates seem to be very successful in their job search and grad school outcomes.
I agree that OP might want to run the calculator and see if they would get money through Rice Investment.