How important is this?

I am a high school junior who is looking to apply to very competitive schools and programs including Ivy Leagues and 7 yr medical programs. Is doing research before applying a significant factor? I do not know if I will be able to get the opportunity to do so, and I want to know how important research would be. If it is, i was interested in contacting my state college and trying to do research, but I know that they prefer undergraduate students for students and that it may be too late. How can I approach them?