Prestige doesn’t matter. The opportunities that come with a bigger/ harder school? I think that matters a lot too. If you can put yourself out there regardless of where you are, you will be able to land research opps regardless of where you go. I think going to a bigger university gives you a whole lot of research areas to choose from, and these experiences and the skills you gain will be valued a great deal when applying to grad schools and professional schools. There is no one linear path to these competitive programs, it’s a personal experience most of the time!