RE: What is the best woodchuck gun?
For long distance shooting I' d recomment a 22-250, 220 swift or a .243. The 22' s shoot flatter, but the .243 is great for bucking a slight breeze. Actually yesterday I was hunting them with a .308, so about any caliber will work.
As far as brand of rifle, everyone will tell you to buy what they have. About any rifle will work. You' ll find a heavy barrel model will generally be more accurate and consistant. That being said, I' d recommend you take a look at Tikkas. I think you' ll find on average they' re better made and more accurate than about anything in their price range.