Personally, I hate whips/crops But when I took lessons I was forced to carry one, eventually I learned three things:
1, A horse that has been disiplined with a whip will change his behavior according to weather or not a rider carries a whip and he will often react at just seeing it move.
2, A whip serves as an extention of the arm, but it has amplified force.
3, the whip should be implemented as a very last resort after all other methods have failed (leg, voice, seat)
I don't carry a crop on my horse, if he is being very stubborn I simply reach back with my fingers spread and gently tap the sensitive spot just behind the saddle. As I do this I squeeze as hard as I can with my legs. It works every time.
As for horses who play with the bit and jerk while standing still, I find that most often the horse is simply asking for a looser rein so he can stretch his neak a little and not have to deal with pressure from the bit. If I loosen the rein and the horse starts to wander or some such thing, I'll retake contact, enough that the horse can feel it but not so much that I'm tugging on his mouth.