I will comment on the football aspect, but I do have a BME major so I have visited Duke, Stanford and Rice. Both DS (football player Ivy) and DD were accepted to Rice. Not accepted to Duke or Stanford (not surprised). Son actually got into Rice from his application only but was told by the football coach that he could walk on if wanted to. He was interested in engineering so Rice was a great fit. However, he realized early on that D1 football is your major. I don’t care what they tell you, it comes first. I know there are kids at Rice that have done it but its not common and its a lot of work and a physical beating. And by the way, its not much easier at an Ivy league. He puts in 30 hours a week in season and there is no special treatment for engineers (chose civil) ie note taking, etc. The coaches want football to be first because they want to win games. The students feel pressure to have to choose between academics and football. This has been our experience.
DD liked Rice due to its locale in Houston near some of the top medical centers in the country, as her interest is in cancer research. We met with a professor in the BME dept and both got the sense that it is very student centered due to its size and has a very hands on approach to engineering.