For the modern guns of today, I would take the good ole reliable 12 Guage 3" pump. #6's for the small game and birds, Size T for larger birds such as geese, etc, and 1 oz slugs for everything else.

For the guns of the time, I would take a 62 caliber smoothbore musket. Get close enough, and take most game animals with the round balls, and use the shot for taking birds and small game.