1. Ignore MBA rankings and take PhD rankings with a grain of salt. There are a lot of way to look at rankings. I would encourage you to look at the other forum posts that address this issue since it has been pretty well covered. I would simply add here that just because a school is highly ranked, doesn't mean you should go there. Rank is only one of many considerations for a phd.
2. Avoid contacting faculty. With over 200 applicants applying each year, you are only going to present yourself as a pest to adcoms. This advice comes from a lot of conversations with faculty.