First, ignore the speeds posted by most air rifles. The posted speeds are shot using very light weight pellets that are not accurate at that speed, the worst at fpe delivery due to shedding speed so quickly, usually not accurate period, and are also harder than your barrel, so your rifling will slowly disappear. A pellet gun is most accurate between 800-900 fps. Find a heavier pellet that the gun shoots well and stick with it. But understand that a heavir pellet makes trajectory more pronounced. A .177 can kill a squirrel, as you only need less than 5 fpe on target.
The main problems will be, you, the gun, and then the animal. Learn to shoot the gun well, meaning get used to the trigger, the way the gun recoils (if it's a springer or a nitro piston it will recoil forward), find a scope that can handle the reverse recoil, and it clear enough and has enough magnification to clearly see your target. Then, learn the drop of the pellet you are shooting. At 800-900 fps you can have a decent MPBR(Maximum point blank range). Download chairgun, and enter information about your gun and pellets, and the software will plot your drop, and your MPBR.
Being that you have neighbors, you should try to drop them in their tracks, which will be a headshot. Make sure that you have practiced shooting acorns out to 50 feet. Body shots can leave runners or crawlers, and it's a quick way to let the neighbors know what you are doing unless they have outdoor cats.
