THe .357 Magnum is not a target shooting load. Continuous use of it will cause the gun to develop cylinder endshake and other wear issues sooner than if you shoot .38 ammo most of the time. Save the .357 for occasional practice and carry when you may need the power. Magnum ammo is intended for defense and hunting.
I advise against using Magnum ammo for home defense. The blast may injure hearing and many such loads have a large muzzle flash that may make follow-up shots in the dark difficult. Use Plus P ammo for that.
Your M-686 is a strong gun, but you can shake even an N-frame or a Ruger GP-100 loose if you fire enough .357 ammo.
When I load .357 ammo, it's usually Winchester Silvertip 145 grain or 158 grain Federal Hydra-Shok.
I avoid 125 grain loads, as they cause excessive gun wear. But it is true that the hotter 125 grain bullets have the highest rating in police shootings. THe stopping power rates about 96% on felons in actual shootings, as good as handgun ammo gets! But a detective here looked at some shootings with that 145 grain Silvertip load I like and said that it is so effective as to almost constitute overkill on humans.
I have a box or two of Remington 165 grain JHP's stashed away in case I find myself in bear country or where Bigfoot sightings have occurred. The bullet is constructed for hunting and not just a slightly heavier 158 grainer. I wouldn't hunt a bear with a .357; that ammo is for defense.
Coyotes and the like don't need those heavy, deep penetrating bullets.