with or with out correction?
Correction is a VERY broad term, as are consequence and punishment. In your original post, many of the methods that you asked for an either/or were one in the same.
Marker training is what clickers are all about. I love this method. This positive reinforcement method paired with a verbal negative marker (in certain circumstances to let the dog know when they're headed in the wrong direction) works extremely well. It has also been proven to be a quick (50% faster learning rate) and an effective method for training, desensitizing and in dealing with behavior issues if used correctly.
I don't believe in or ever use any intentional physical correction. This is one reason that I never use aversive collars such as choke chains, pinch/prong collars or shock collars. These aversive tools create an all to easy and common setting for poorly timed correction whether intentional or inadvertant. Control, when needed can be attained with pain free tools like no pull harnesses and newtrix collars, though I'm all for training first whenever possible without the use of special tools.
Although I work with extreme cases, I see no need or use for physical punishment in training at all. Consequence to me simply means a predictable cause and effect exchange, it does not ever have to mean anything physical.
So I guess to sum it up I would go with (from your original list) -
Marker trainer (click and treat - which is faded quickly)
with verbal negative markers.
By the way, during an Ian Dunbar seminar the three methods (positive only, positive with negative verbal marker and positive with positive punishment, (leash corrections and such) were demonstrated. The positive method with negative verbal marker was far and above the most effective method of the three. Postive only made for confusion and took considerably longer than with a verbal negative marker, and positive with positive punishment had the dogs shutting down..too affraid to throw new behaviors for fear of correction.
I have, over many years, used all three methods as well and find that positive reinforcement with verbal markers to be the most effective method that I have ever used. This method carries the least risk of negative effects, is extremely versitile - and is FUN as all get out
....I'll never go back!