What one thing ruins more pictures than anything else? The blur that results from an out-of-focus image. Holding the camera correctly can help prevent that blur. Wrapping your left hand over the top of the lens makes it less stable and more likely that you’ll move the camera while shooting.
If you’re going to have merely milliseconds to capture expressions, and maybe a little longer for poses, you need to look to fast lenses and high shutter speeds to help you out. You also need to work quickly, so complete familiarity with whatever gear you’re using is vital. The worst thing in the world is an amazing moment happening, and you’re at the wrong setting or just not ready.