+1 for a bull barrel Ruger 10/22. With a halfway decent scope, you can hit anything at almost any range.
Personally, I love CZ weapons. I have several and my dad has dozens (he has a fire arms sales license).
If you are positive you will get a scope, then I would suggest a CZ 452 varmit. Alternately, the CZ 452 scout (on a budget) or the 452 Style (if you like nickel barrels and black polymer).
That being said, I would also suggest that you look at the Sig/Hammereli Trailside. Yes, it's a pistol, but it's a Hammereli pistol. It's about the same price as the rifle and the 6" barrely is probably just as accurate as the rifle out to 150 yards. With a scope, it'll go much farther. I put 9 rounds in the top of a coke can at 60 yards with iron sites (they are adjustable).
Hope that helps and let us know what you get.
Oh another REALLY fun one is a Puma (yeah, I know, but trust me) lever action .38/.357. The pistol ammo is cheap and it's a lot of fun with the lever action.