RE: .243 or .308
Well, for birds and coons a 20 guage shotgun would work pretty good, but for ground hogs and well, coons a 243 would probably be the better bet. A 22 would probably be an even better thing to buy for that kind of shooting, it works wonders on any of those pest and is a hellava lot cheaper to shoot than either the 243 ot 308. Not to mention it sounds as if you are pretty fresh into shooting and a 22 is a great starting point.