We only have a couple of rimfires here on Kena Farm. My favorite is my Marlin 925M (I know you said .22 LR/L/S, but this rifle is available chambered for those also). It was very affordable to buy and topped with a Simmons 22 Mag 4x scope, it is our go-to rifle for racoons and coyotes (we keep poultry). Scope and rifle were bought about 14 years ago for less than $150. As a bonus, these rifles break down very simply and trigger work is very easy to perform. The newer version, the XT-22 is very close to being the same rifle, but has a slick adjustable trigger. I'm partial to box magazine-fed rifles like the 925, as I find them safer to unload. They also are able to fire longs and shorts...if you can find them...and is not sensitive about un-jacketed ammo.