CotW has changed a lot since release, and small game--mostly absent at the start--now make up a significant portion of the species. But as it stands there are no rifle or handgun options for Class 1 animals without buying DLC, leaving new players to unlock either birdshot or small game arrows.
I think adding a combination gun chambered in .22LR and .410 shells would be a great way to bring those cartridges into the base game while not making any of the DLC guns which use them obsolete. Players would be able to hunt small game from the start, but the break-action means they wouldn't be able to spray-and-pray at whole flocks.
Pictured are the Savage Model 42 on top and the Chiappa Double Badger below. While in real life I'd gravitate toward a gun with wooden furniture I think in the game I'd prefer something based on the Savage. It's marketed as a youth gun and that would jive with its status as a starter weapon in the game. (edit: Another plus for the Savage is that instead of dual triggers you flip the hammer to choose a barrel, meaning there would be a visual indicator of the swap for the player.)
And lastly, one of these should be added just because combination guns are cool, and the Grelck could use a buddy (though, uh, just make sure all the issues are fixed with that one before adding another).