For varmint shooting, I would suggest a .223 / 5.56. I suggest it due to the ammo availability, the plethora of platforms that will shoot this caliber, and my personal opinion that anything bigger is a bit much unless you want to shoot at ranges of over 300 meters. As for firearms, Id honestly go with something based on the AR15 / M4 line of sporting rifles. I suggest that breed of sporting rifles for the nearly infinite numbers of ways that you can customize it. For varminteering you might want to go with a 20" stainless steel barrel for improved accuracy that you just cant get with a chrome lined barrel. Just keep in mind that stainless steel barrels also wear out a lot faster. But no matter what rifle you get, if you will be shooting at long distances, make sure you invest in a good scope. Dont cheapen out on this area.