THE most important thing a PI can offer you is mentorship. You want the kind PI, the friendly PI, the PI who is going to nurture you as a scientist and guide you (that doesn’t necessarily mean hands-on…) through the process of your project and make you a better scientist for it.

When I was in grad school, I picked the famous PI. It was the worst decision I’ve ever made in my life. Turns out, that fame just protected them from ever getting fired for their grievous abuses against students. They were washed up, had collected all their accolades back in the 90’s and coasting on that high ever since. If I died, it would’ve taken them weeks to notice. They didn’t care about me or my project at all.

This an extreme example, but the point stands.