One of our regional high schools' students consistently place highly in Intel and Seimen's competitions. The top prize a few years ago went to two students who worked over a summer and then the fall term with a major researcher at the prestigious medical school nearby. No doubt, these kids are very talented. They were fortunate to have terrific mentors in the PI of the lab and a graduate student who taught them a great deal. So, while the projects are judged on the students' presentations, it helps tremendously if the students conduct research in a high-power lab with NIH funding and a project already in later stages of development. This particular high school essentially matches interested students with mentors at the university/medical school in town. The facilities available to these kids cannot be matched by doing experiments at home, or even in a lab at school. Sophisticated gene sequencing, PCR, Western blots, etc, are not something you can do in your basement. Occasionally, there are big winners with home-grown projects, but if you look at the top projects, they often are supported by major facilities and grants in medical schools or university-based research labs. That's not to say a home-grown project wouldn't be worthwhile.
My D's teacher at her summer talent search program mentioned the Young Epidemiology Scholars program. It's something to consider, although you have to be in 11th and 12th grade I believe. When I looked at the projects, my impression was that these could be done by students without a lot of equipment or materials. You might want to check into it.