For college pitchers, their pitching coach will be their first boss in the adult world. This is the guy (or gal) that is going to make you better in theory, and give you more tools to compete.
My son and I looked & talked to many dozen pitching coaches when he was being recruited. We saw two kinds of pitching coaches. First is the PC who is going to take what you've learned to this point foundationally, and teach a player within the player's own framework. The second type of PC is going to scrap the players foundation, and teach the player based on the coaches foundation (we called this the cookie cutter approach). Essentially, it is like a house. Are you going to build off an existing structure or tear the structure down to build something "better" in theory. My son preferred the first type as we believed his mechanics were the strongest part of his game. The best PC's can do both methods.
Chemistry between a recruit/player with their pitching coach or position coach is absolutely at the top of my list. Trust and a logical approach to pitching were an important combo that my son was looking for. His pitching coach was a crafty lefty who knew how to best communicate even though my son was a RHP. Everbody's situation is different, and I think my son felt the most comfortable with that type of pitching coach.
JMO.