Beeman R9 in .22
.177 for feathers and .22 for fur. Get the German stuff. Beeman R9. I use a HW50S .177. Its good up to squirrels/rabbits. Wouldn't try a groundhog with it. .177 is cheaper and some think more accurate and balanced in a airgun. Flatter shooting too. Don't be fooled by outragous velocity claims by the lower tier air gun companies. For what your wanting you just can't beat a R9 break barrel in .22 The more power a spring piston puts out the harder it is on the scope and the harder it is to get a accurate shot out of it. Hold sinsitivity its call.
On the PCP biz some like them some don't. You'll need a $$$ air pump, and they seem they are allways leaking air. Also when you put lots of humid air into a tube the water starts to slosh around. So you then get a $cuba tank and find a place to buy clean dry air at dive shops or fire houses. In the end you'll sell all that and just keep a R9.