One gun, one caliber

Impact M3 Sniper .25 shooting NSA 36.2gr slugs @980fps for long range varmints. 
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First consideration is caliber. IMO, the .22 or .177 would be best because pellets in those calibers are most common and more readily available than the larger ones. True, the 25 or .30 cal has more oomph, but if you can's find ammo, you may as well use the gun as a boat anchor. Next is the gun. A stand alone type such as a spring piston or pump up makes more sense. What happens if you run out of air for your PCP? What happens if there's no electricity to run your compressor? Hand pump? Maybe.
 
For me, the .22 caliber strikes a good balance. The pellets are large enough to handle, large enough to see on my targets (I'm an old guy), and provide enough power to take most pests. 

Most of the rifles I've had are in the medium price range. Of these, the Wildcat III compact is my overall favorite; my go-to gun. Easy to carry--short and light--so good for hunting, and not bad on the backyard bench.