They're looking for the same things, and have the same standards as the rest of McKinsey!
Overall, you need to be a strong candidate. This means, in general, you come from a top school, have a high GPA, have a good amount of experience in the business world (running teams, projects, solving business problems, etc.). Of course, it's much more about the whole package than any individual item. Feel free to send me your resume and I can tell you if you're a strong candidate or not!
In terms of getting connections, this isn't really the forum - everyone here is tryig for connections (and coaches won't just "sell" you referrals)! Rather look to network (primarily via LinkedIn) to build these connections!