I appreciate all of your enthusiasm. It is always great to have a new comer who asks questions. You will not need to worry about shooting anything at 1,000 yards, however, regardless of what it is. Even out west, a 400 yard shot is an extremely long shot on anything. The vast majority of people are not qualified to even try such a shot, and much less do they have a rifle or shooting technique that is accurate enough to try it.
Groundhogs are a woods/mixed fields animal. In all of my years of hunting, I have never seen a shot over 250 yards on a ground hog, and I have never taken one over 150 yards. You certainly won't see a shot on a ground hog over 150 yards in the state of Florida. And, to be honest, I am not sure if the ground hog even lives in the great Western states.
Prarie dogs are about 1/5th the size of ground hogs. I know that out west, with extremely tricked up rifles, very high powered scopes, and hand loaded ammo, people probably shoot these at 400+ yards. But, you won't be doing it with any "all around" hunting rifle. You will need an extremely specialized varmint rig, and lots and lots of practice.
I believe that the weight of advice from others here is very very sound. For varments, get a .223 Remington varmint rifle, learn to shoot it well, and you will never regret it. For all game larger than a coyote, and up to and including moose and elk, get a .308 Winchester, learn to shoot it well, and you won't regret it.
Good luck and good hunting.
Big Paulie