I have a Gamo Maxxim I picked up last year just for the squirrels tearing things up. Have shot a dozen of them and it has worked great and is accurate.
Ive got a gamo that I used to teach my daughter to use a scope. Its a bad dude and with the platinum pellets I bet I could kill a small deer. The only problem is it as loud as my .22. Id look at one of the ones that is maid to be quite, like that bone collector model "quiet cat".
ive got a Benjamin Nitro in .22 and it'll dispatch most pests VERY well. Crossman Premier hollow tip pellets seem to be the most consistent, shot groups inside a 1/2" at 25-30yds out of the box. the trigger is adjustable but still a long pull, with a trigger upgrade i think i could tighten the groups dramatically. the nitrogen pistons are more accurate and consistent than the springer models. as Churly mentioned if you get a .177 and use platinum pellets you will get the sonic crack. i like the .22 for the little extra punch when you hit them