A lot of pitchers, and people in general, don't have as much dexterity in the index finger compared to the middle finger. Your middle finger is your longest and strongest finger. You see a lot more spike curve and one-finger curve grips these days. Not many pitchers are throwing a two-finger curve. Neither grip is better than the other. Pitchers use what's comfortable.
As for the circle changeup, you want the index finger off because you are trying to put less force on the ball by throwing it off the middle and ring fingers. Throwing it off the index and middle would be a fastball. Although, some pitchers do throw a three-fingered change. The reason some pitchers can't throw a circle change is because the ring finger doesn't have much dexterity as the middle finger. In this case, some pitchers choose to throw a splitter or forkball as their changeup. Although, some pitchers throw both, like Smoltz, Hudson, and Haren.
As Bower and Zita said, sliders and cutters are thrown off the index finger.