As simple as this sounds, the way the pick is held may have some repercussions on the speed and accuracy of string engagement.
I have been experimenting with three techniques:
1. The pick is held between the thumb and the left side of the pointing finger of the right hand.
2. The pick is held between the thumb and the pointing finger.
3. The pick is held between the thumb on one side and the pointing and the middle finger on the second.
The first technique is used most often. The problem with this technique is the right hand either has to be twisted a lot or the elbow of the right hand has to be positioned to the middle or the lower of the guitar body in case the player desires to put the pick in parallel to the strings. Obviously, in case the player prefers to put the pick to an angle to the string, then there is no problem.
The second technique is also used a lot and eliminates the problem previously described as well as allows for any angle of the pick towards the string as well as being in parallel.
I love the third technique a lot. The third technique is basically the same a the second except the third technique provides a better mechanical stability. Also, because of the mechanics of the fingers of the hand, the third technique psychologically inclines the player to position the pick in parallel. Obviously, the third technique does not preclude the player from positioning the pick at any angle towards the string in the 3D space.
Another slight advantage of the third technique is a stronger grip when large, triangular picks are used as well as a standard pick is used to play not with the sharper, playing edge but with one of the more rounded, non playing edges.
For more on picks and techniques, refer to other articles I have written on the subject.