I got bored of rifles and went to .22 handgun hunting, myself. My 10/22 is minute of squirrel to 50 yards, but my old Remington 512X shoots rings around it as does my 10" Contender .22 match barrel AND my Ruger Mk 2.
For a small game rifle, the Marlin M60 is accurate and cost effective and out of the box, will out shoot the 10/22. My Remington M597 magnum is 1.5 MOA accurate, but I'd get the .22LR model for squirrels. The magnum is a bit much, will kill squirrel of course, but it's like shooting deer with a 600 NE, except for recoil.