Sounds like you have thought this out and know exactly what you are looking for. Far be it from me to try to change your mind on any aspect of what you seek.
Your criteria pretty much rule out the J-frames and the SP101 - they are all 5-shot. Also, while nothing in 357 is really a "hand cannon" the smaller 5-shot guns make magnum rounds
feel more like a hand cannon because of their reduced weight.
The S&W models 586, 686, 13, 19, 65, 66 all meet your requirements. I tend to agree that the 3" models would best meet your concealment criteria, and are a little better for easy handling from a holster, though they tend to be at the upper end of your stated budget or even slightly higher. BUT, good deals can be found. 4" models are slightly harder to conceal, but would work with the right holster.
The 586 and 686 "plus" models even give you seven rounds - exceeding your stated requirement of at least 6. But again, they tend to be a little higher in price than the 6 round versions.
As others have mentioned the models beginning with a 6 are all stainless steel, which is good for corrosion resistance for a gun that will be carried in the field.
For my money, and to meet all your criteria in spades, the 3" model 13 or 65 seem to rise to the top of the list. They are 6 shot, K-frames so they handle the recoil of the 357 just fine. They have fixed sights and 3" barrel which makes them better for concealed carry - and presentation from a concealed holster. The 3 inch barrel doesn't compromise velocity nearly like a snubby would, and gives adequate sight radius for accuracy.
The only problem with the 13 is that it is scarce, and the other benefit of the 65 is that it is stainless. So, all things considered I would recommend the model 65 with a 3" barrel. Of course I must admit to being a bit biased. The one in my avatar is my favorite revolver.
