I do not shoot single action revolvers and have no experience with them. On the other hand, I shoot double action revolvers a lot.
I have been using the .357 magnum for over 30 years and my experience is that you should AVOID ANY S&W K-FRAME as a .357 magnum. They make great .38 Special and .38 +P revolvers, but have the problem with the ground off forcing cone and a thin topstrap. My agency issued me a S&W model 13 K-frame with a 3 inch barrel and round grip (ex-FBI guns), several years later, we had a forcing cone crack when qualifying with the 125 grain jhp with a model 13. This was a wonderful carry gun, but just not strong enough in my opinion for continued use with .357 magnum.
To put this in perspective, my agency required a minimum of 500 rounds a year of .357 magnum to qualify. We also shot some .38 Special, but not often.
If you want a mid size gun, I recommend a used RUGER Security Six. Just compare a model 19 and Security 6 side by side and it is just no question which is the stronger gun. The ground off forcing cone on the S&W is not on the RUGER and the topstrap is much thicker ( I noticed that the new COLT KING COBRA also has a thicker topstrap than the S&W K-frame, but is a light gun). I know a lot of people will argue against this point of view. I do not care, this has been my experience with several K-frame guns and Security 6's.
I bought my last one for $349.00 used. It had a trigger job done, but is 100% reliable.
If you are willing to go up a size, then either a S&W L-frame like the 686 or a RUGER GP-100 are great choices. They are strong to the point of being overbuilt for the .357 round and now both are available as 7 shot revolvers. The S&W L-frame can also be had in .44 magnum, if you will accept a 5 shot revolver.
The full size N-frame S&W revolvers and the even bigger RUGER Red Hawks just weigh too much for most of my use and usually will cost more than $500.00, even used.
I really like the S&W K-frames and some of my favorite range guns are a pair of model 15 Combat Masterpieces and a model 19 Combat Magnum, but they only get standard pressure .38 Special and occasional .38 +P for self defense. The S&W L-frame is a terrific .38 Special, but is borderline for the .357 magnum round.
Jim