What you should get, however, is the rifle. You'll be replacing them entirely soon enough.
Though a word of warning: upgrading your shotgun and pistol right now is not a very good idea. Exit the shed and run around to the back of it to meet up with a merchant-if you've got some cash to spare, consider picking up some items and upgrading weapons. As you exit the small shed you're in, you'll see through a window a mysterious figure.