Hi Craig
A number of the bigger scope manufacturers make good quality, .22 specific scopes. These scopes usually differ from normal scopes by having parallex set at 50 yards rather then 100 - 125 yards. That said, I have used centerfire scopes on my .22's for years without problem. Weaver, Bushnell, Simmons, and Leupold come to mind.
I like a 2x7, or straight 6x on my .22 rifles, though some shooter like much higher magnification for precision head shots, though I have not found that to be really necessary. In optics, you tend to get what you pay for. Don't waste your money on $25.00 scopes. $100.00, or so, will get you something decent. Look for at least 1/4 minute adjustments - a squirrels head is a small target.
Larry