I did a degree in CS first and then graduate school for Biomedical Engineering. It was a good path for me. Solid programming foundation in CS (and a lot more)

I did a degree in CS first and then graduate school for Biomedical Engineering. It was a good path for me. Solid programming foundation in CS (and a lot more) with experience and domain knowledge applying it in graduate school. Leading a research with grant with the US government (NIH, NHS, DARPA, etc) generally requires a PhD. You could probably be a PI without but it would be scrutinized. Graduate school in any math/science field will give you the experience needed for research, and gaining the domain knowledge is extremely helpful. If by research you mean "scientific computing" then you can easily do that with CS. My first job out of undergrad was supporting research efforts with data acquisition and analysis. If you know that's what you want to do go strong with math and statistics as a CS undergrad.