For squirrels, you can get by with a basic .177 springer. I killed a bunch of them growing up with a Gamo break-barreled that I fed RWS domed pellets. More expensive PCP models can be more accurate and more powerful, but the nostalgia of hunting with a break barrel drove me to get a WH95L in .22, and it is a dream to shoot. Slower, heavier pellets seem to be more accurate for my .177 and the .22. Velocities from 600 fps to 900 fps are plenty fast for killing squirrels.
For pellets, the predator polymags, H&N crow magnums, and JSB exact pellets all seem to do well. The polymags and Crow magnums actually expand quite a bit as well.
Those german made springers are a ton of fun. The HW30S urban pro is a pretty cool model that comes with a scope and suppressor.
The real trick is finding a scope that can survive the punishment and not shift in the mounts. I ended up using Form's scope-mounting guide for rifles and degreasing, then torquing everything to keep the scopes from shifting. Also, witness mark the scope and the mounts so you can tell when things have shifted.