So, you want to be a PhD student or a postdoc at an R1 university. Let us quickly review why.
They tend to be well-resourced and do some cool research. They also tend to be great places for networking.
The labs tend to focus on papers and grants. They tend to be less good at teaching than a lot of other places.
Applying to the wrong lab will not get you an interview and if it does this will not lead to an offer. So lets dive into what are the right labs: