I think lobster picnice is on to something here, juse my opnion. My uncle has a 686, actually 2, a normal one and the newer SSR (I think that's the style) . While I like his guns, I have a TRR8 I use for hunting, plinking, etc. It's literally the most versatile gun I have. It may seem out of your price range, but stay patient and look for one used. My trr8 out shoots my uncles 686, not by much, and maybe because I have a red dot, but this is the point, I can have a red dot, so for hunting it's perfect. I think the shrouded 5 inch barrel is thereason it shoots well, too. I also have a 66-1 4" that I like, but the 4 seems too short for hunting, the 6 seems akward and sometimes a bit long, the 5 inch seems the perfect size.
Also, I can use it for night hunting, or just as backup for night when using my night vision, as I have a Streamlight IR and visits light I sometimes attach. This obviously makes it a great home gun, too. Not just a hunting pistol.
So it's setup for optics and light if you need, but don't have to if you don't want to.
I'd say your correct in the 357 dept for hunting. You can take small game with 38 spl, and up to deer if you know what your doing, which I believe you do. I load my 38 spl to what feels like a 22lr, and doesn't blow up bunnies or coyotes and such, so you can keep the fur. The 357 is strong enough though for pig and deer if need be. I'm an opportunity hunter, meaning, if I see a deer, I may or may not take it. If I see a rabbit, I probably will take it, basically, I love that with my pistol I have choices when out, so never bored or think damn, a rabbit, wish I didn't have my 44!! I have a 44 mag that I haven't seen in a long time since getting the 357's.
Obviously this is all personal opinion, as you need to find something that fits you personally. I will say that my smaller 66-1 feels like it weighs nothing, and many hunters use the 19, same thing but blued. It sits nicer on my hip and very comfortable, but my trr8 gets the pick over my 66 everyone because of its versatility and accuracy. The 686 is a great gun as well, clearly. I have a Ruger super redhawk, but that thing is humungous, and the gp100 is a nice gun, but I do know what Smith guys talk about when they poo poo rugers. I used to just think they were snobby, but having both, I'd choose the Smith's over Ruger.