Decide the job first, then the gun, then the cartridge. This plan sorts the shelf by what you want to do.
Plinking and small game
For practice and small game the .22 LR is the standard, and 40-grain loads are at 22lr 40 grain ammo. The .22 Short is a quieter, gentler option at very short range, and its loads are at 22 short ammo.
Varmints
For prairie dogs and ground squirrels, the .17 HMR...
