I think your choice of a shotgun with interchangable barrels is ideal for your situation. You will be able to do just about anything you want with that gun, so long as you do your part to work within your limitations. You will be able to use that gun to hunt deer, elk, moose, caribou, black bear, and many similar big game species, as well as turkey, waterfowl, upland birds, and varmints. You will have to keep in mind the effective range of that firearm for big game is going to be less than 150 yards, but most big game are taken at shorter distances anyways. The various Mossberg configurations do quite well for all the different bird and close in varmint hunting needs, and the Mossberg actions are basic, rugged, and reliable. Consider also that the same gun equipped with a 20" barrel is a most effective self defense tool for the home.

Like others have said, I would strongly recommend getting a 22 rifle as well. It will save loads on target practice and be much more pleasant for you to shoot, and has a number of good uses as well, for not that much money.

Centerfire rifles are generally more effective for harvesting big game, especially at longer distances. But the rifled bore shotgun is a darned good compromise, and has put plenty of venison on people's tables. A one ounce slug with a muzzle velocity of 1,500 fps is a quite realistic load, and generates over a ton of energy. It is only slightly less than a typical 308 or 270 hunting load.