Well, I'm no expert in stuff, and a lot of things in red dead can come down to personal preference. But I'll drop my two cents
Personally, I found the best camp location for hunting to be the great plains. It has enough open area to easily hunt and a decent amount of things that spawn (including bison, which I find great for easy pelts).
For weaponry, I definitely feel that one of the bows is a great investment, especially if you often find yourself using paint it black. As it doesn't actively harm the pelts of smaller animals.
A rifle is also very useful. I feel a bolt action (or Carcano at higher levels) works great. But I have a friend that enjoyed the Springfield, so again it's a personal preference.
You should get all the different trader wagon sizes, because they allow you to do larger sales. Those upgrades are an absolute must. I'd also highly recommend the stew pot, as it's both easy dailies and easy gold cores when you start the session. Other than that, personally I don't really see a 'must buy' upgrade... except maybe the hunting wagon, as it allows less back and forth when hunting.
Dead animals will rot as far as i recall, so you'd just have to turn them in quick or store them in a hunting wagon. Alive animals can be not damaged by either using a bow, or aiming for the head with an insta-kill (like a rifle)