Rankings themselves are not important; most universities understand that they are biased and often poor indicators of what happens at a university.
One advantage of graduating from an undergraduate institution that is active in research is that the professors who write letters for you are likely to be well-known. If your undergraduate degree is from a school with less well-known researchers, the reviewers don’t know any of the letter writers, and you don’t have published research, your chances of being accepted into very competitive programs might be lower, because it will be harder to interpret recommendations from letter writers.
Also, keep in mind that admission committees know that some excellent undergraduate programs grade harshly and a 3.5 GPA is actually pretty good. Hence, there is no simple answer on how the ranking of your undergraduate institution impacts your admission.