Hunting, I find, is easiest with high skill in stealth, and to go naked with a woodsman's axe. The trick is that you go hunting at night, in the later afternoon or early night there's still enough light to see some distance when you climb a tree, so you can spot creatures on the overmap. Then approach them, and begin hiding. Creep forward while they're asleep, and when you get next to them, perform a death blow on the neck. Severe the head in one blow. Works well with high strength, but I always go Owl Tribe because they're good with bows and stealth.
This works particularly well with bears, since they go to their caves frequently. It becomes less 'hunting' and more 'shopping' when you know where the sleeping animal is.
Also: Set out plenty of fox traps. Fox furs are the most valuable to foreign merchants, with a low-weight fox fur being more valuable than a high-weight bear fur. Trade for good weapons and armor. Keep your bear furs to make your own clothing, or to make footwear and sell.
Invest in a hunting knife. They inflict bleeding wounds. A fleeing animal will leave a trail of blood that you can follow until you find them bled out and dead, ready to be collected.