Yes, the PUNCH. Through out the whole history of MA any where in the world, no other subject (except perhaps sex and chi) has generated more argument.
Why? because it is THE most used item in any fight, and we all know in any fight, the variables are so, well, varied that there cannot be a one-size-fit-all answer.
My views are:-
I agree substantially with Reaperblack (I did roughly the same research many years ago)and modified my own training accordingly as a result of a bad combat injury of the wrist.
Of the full twist, 3/4 twist, vertical, even the 'pinky' punch, there all have their place and time in a fight. Added to this will also be that for every type of punch, there is a specific conditioning method tailored for it and a special way to execute it so that you won't suffer the kind of injuries commonly associated therewith.
I'll skip the specific training methods for each; suffice to say, it involves a lot more than just striking the makiwara and tiger claw push-ups. It will require a mini manual.
But let me touch on the full twist punch. The best place for this punch is in two basic scenarios.
one, when a lot of arm-power is not available because the available target happens to be near AND not directly in front, but awkwardly to the side. The power will be all from a waist-torque. No so-called 'snapping' or 'whipping' here as the distance travelled is very short and you want to put a punch in quickly before the target moves.
two, the long-range snapping or whipping punch, the so-called boxer's punch, but with a full twist. Here the target is far away and to reach it you need to extend your arm until your elbow is a millimetre shy of being straight and the only power available to you is the snap or whip at the end of the punch. This will be to soft targets like the stomach, liver areas. Needless to say, a lot of specialised training is required to make this work and not hurt yourself. The good thing about this punch, with proper specialised training, is the blinding speed from any originating angle because of the absolute absence of opposing arm muscle antagonism by way of full relaxation of the triceps.
Now, the vertical pinky punch. I will use this punch on only one occasion. When the opponent is a lot taller and I am going for his chin, when the upper-cut is not necessary because my pinky is already quite near. Here, my thumb will be resting on top of the index finger instead of the normal curl. This, besides being able to tighten the pinky more, will also harden the tendons on left and right side of the wrist.
There will also be a tilt of the fist when in the full vertical position.
As Reaperblack has already taken the two cents slot, I'll settle for 2 1/2 cents?