+1 on the Blackhawk. Airgun Depot has a Ruger Blackhawk (air rifle, not the revolver!) 177 pellet rifle for $59 plus shipping. Yes, it is a refurb, but these are normally fine. It has a synthetic stock you may want to fill with something to add weight. As you've learned (since you are looking at the QB's as an alternative), spring rifles do recoil and are not the easist to shoot. The weight helps. Or get the Ruger Airhawk, same rifle with a heavier wood stock. Those are the down sides. Here are the nice features of this air rifle:
It is an excellent clone of the German RWS34 air rifle. Most internal parts, like springs and seals, are compatible. This is also the same rifle as the Xisico BAM B25.
It has an outstanding trigger. Gamos and Gamo clones like the Crosman and Stoeger spring rifles do not. There are after market fixes for the Gamo trigger, but that will run you another $30 or so.
It is about a 14 fpe air rifle (~900 fps with real 8 gr lead pellets - start with Crosman Premier Light 7.9 gr dome pellets as these work well in many rifles). Plenty of energy for your pest problem.
The price.
You can always send it to Mike (
www.flyingdragonairrifles.org) for a tune later. Mike also is buying and tuning these for resale now. The web site is a work in progress, but has his phone number. Best to just call him.
Amazon has good deals on air rifle scopes and mounts. For your use, check out the UTG 4x32AO (aka Leapers) and medium height UTG scope mounts. $45 will cover both, shipped. This is an airgun rated scope. The scopes and rings that come on most air rifle combos are garbage by comparison.
If you get a springer, be sure to clean up the stock to action holes with alcohol, blue loc tight the screws, and wait for it to set up. I do same with my scope mount screws. Clean the barrel with Goo Gone, and a patch run through weed wacker line with a not on one end. Air rifle barrel steel is not as hard as powder burner barrel steel, hence the weed wacker line vs cleaning rods. Goo Gone won't disolve air rifle seals like Hoppes!
And yeah, don't dry fire a springer. Another way to give one an early death is shooting lightweight alloy pellets in it. Stick with lead pellet weight around 8 gr for 177. The spring driven air piston slams home too much with the light alloy pellets and will destory the air seal a shot at a time.