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.

I would recommend studying a career heavy in applied mathematics. I'm an aerospace engineer and I have worked on hydraulic simulation and UAV navigation before further studying machine learning and working as data scientist. The most important skill I have learned is mathematics.

Also interested. I can find job offers, but probably lack qualification. What would be the best way to learn scientific or research programming and data science?

Either have a friend working in a lab, or find a lab you like and ask to volunteer for a bit, if they become reliant upon your work (and if you become an author on a paper), you have leverage to ask for a position. You can always leave, and if your lab was particularly known for something, then other labs will want you to work for them as well. This is what I did (although I wasn't particularly looking for a job, I just found the work they were doing interesting and I wanted to get my hands dirty, I also dont have a degree so maybe if you do it will be easier to navigate the academia bs), and YMMV.

I got into the field of scientific oil & gas software just through being in the right area of the world - Perth, Australia which is a hub for Oil & Gas exploration. Prospects are not great these days though, due to the resources downturn. I've since moved into another area (health).

Get a degree in math, physics, biology or chemistry and a minor in CS. Learn databases and write any kind of remote API. Learn how to use a batch system and MPI.

Then learn how you can make this ghetto better and look at labs and universities for a job.

For what keywords should you search job listings?

(I happen to have a PhD in mathematics and decent programming experience. But while transitioning to private industry, I never came across this type of job or failed to recognize it.)