It is often said that .22's have killed more people than any other caliber. They may not stop a person determined to do you harm, but they may eventually kill them. Israeli execution teams used .22's after Munich.
How deadly depends on what you are hoping to kill. The smaller the varmint, the lighter the bullet. Hollowpoints are deadly but they make a mess of the meat. For larger varmints the Aguila Sniper Subsonic, which I have used, does nicely IF you are a darn good shot (head or other vital organ). The heavier bullet penetrates better -- but only if shot from a rifle (a revolver does not due justice to any .22 LR).
If you are set on .22LR, then the above suffices. If you want a .22 rimfire (especially if your local, state or other government has rules or regulations against centerfire), then the .22 magnum (WMR) is the best way to go. There have been lots of poachers of deer which have used .22 magnums because they are quiet. But they're not as quiet as .22 Sniper Subsonics. Close stalking and acccurate shot placement are crucial. If you're good at those skills then maybe archery would be the way to go (but you can't stuff a bow in a holster under a jacket).
That looks to be where I will concentrate my purchases.
.22 Magnum is an oxymoron.