Or maybe a .223? I guess that might blow away some meat, but it would also be effective for smaller predators, and other... "midsize" (?) game.
Here in GA, only .22-cal rim-fire or smaller is legal for small game hunting, along with shotguns. I would purchase both, but if I had to choose one, I would go with a 12ga shotgun because it is the most versatile.
I just looked up VA hunting laws - Wow! What a confusing mess. Looks like in some counties, your .223 would be legal for small game, in some you can't fire a rifle at all except at an approved range.