I place the highest emphasis on the grip when working with almost any student. If the player is advanced, I probably would not change the grip. However, with everyone else I most likely would. How the hands are placed on a golf club will influence everything that comes after. For this reason, I believe that the first lesson is the most important lesson in any persons golfing life.
For example – if a player has a strong closed face grip, they most likely will set up with the hands very forward and aiming to the right. I prefer a simple, square set up and aim position so I can keep the swing technique simple as well. If a grip is open faced, then the player will most likely flip their hands at impact to keep the ball from going right. If it is closed face, then the player will most likely hold on and not release to prevent the ball from going left. For these reasons I teach a hand position somewhere between neutral and strong neutral.
As for the style of grip, I start my younger players and women with the 10 finger or baseball grip. This seems to help them control the club a bit more and thus have more connection to the club face. After that, I try and work with the student to develop a grip style that feels comfortable for them, which could very well stay as the baseball grip if they are successfully improving.