I think the best hunting sidearm for your bucks is a 6" barrel current production 629-6, SKU #163606. You can remove the rear sight by taking out one screw - and mount, with blue Loctite on the three screws, a Weigand SS rail. Add some rings and a scope - and sub some S&W/Hogue .460/.500 Magnum monogrips - and you have an easy to tote distance rig. Regular iron sights are fine, too - if that's your forte. Modern S&W K, L, & N frame revolvers are pre-drilled for a scope rail.
Yeah... it's not a .357 Magnum... it's a .44 Magnum. If you like lead, you can load some 240-300gr loads at 900+ fps - not 'real' Magnums - but effective. It weighs .1 oz more than a 6" 6-shot 686... an ounce more than the 5" 627PC mentioned earlier. I haven't hunted with mine - actually, I haven't hunted in decades. But my 6" 629 is a keeper, even if it seemingly wears that scope for only a few days before I tire of it! Besides, while some states/locales require 6" barrels - many also require calibers >.40 for handgun hunting deer, etc.
Stainz
PS I love my 4" 627 Pro and snubby 627PC's, but the only 6" .357 Magnum I have is a 66!