You need to hit 'M' and go to crafting, then hover over the "weapon holster" (the first one) and look at the bottom right to see what animals you have to kill and skin to upgrade it. I suggest the bow, its fun and you get 2 skins instead of filling the animal with lead and getting 1 skin. Rhinos on the other hand are really really tough, you have to buy the elephant gun which is what I did (its under signature weapons tab). The strong shotguns should do the trick.