I love my .44s, but a .357 will work for what you want it for. Plus, it will be a lot cheaper to practice with since you can practice (and hunt small game) with .38 Specials. Deer hunting with a .357 will be fine, too, if you stick to bow hunting ranges and use 158-gr. (or heavier) bullets. Many a black bear have been taken with .357s. What ever a .357 will do, a .44 will do better, however, I think a .357 will be better to start out with. Once you are use to magnum loads without flinching, then move on up to the ones with the really big holes in the front end.
For an all purpose woods gun a 4" or 6" will work just fine.
I like the Smith & Wessons because you can get night sights for K,L, or N frame guns. Out in the woods at night it can be difficult to see your sights. I've got a nice little (yeah, right) 4" .41 mag for my woods gun. It's got night sights and is a real tack driver with 240-gr. Winchesters. Perfect for things that go bump (or growl) in the night!
Let us know what you decide on.