I shoot a lot of rimfire calibers. The most common is 17 HMR. From my gun and a stabil bench I can easily pick them off out to 200 yards.
My rifle is a Marlin that I put a Green Mountain Bull Barrel, and an enhanced trigger.
I also shoot 17 Mach 2 , and 17 WSM. The WSM is based on a Nail gun cartridge and is more powerful, and the 17 Mach 2 is based on the CCI Stinger case. [ just slightly longer than 22LR] It works great on squirrels out to a little beyond 100 yards. and its quieter than the 17 HMR.
If you are new to them the two rimfires Id look at are upper end 22LR, and 17 HMR. They are the most common and the easiest to find ammo for. I combine good glass with a sturdy bench and I can push out the range a bit. My 17 HMR wears a 6x24 Nikon Monarch. Some people laugh at that size scope on a rimfire, But if I can see it I can hit it! DR