All good advice so far, especially the part about making sure it's appropriate for rimfire ranges. Another consideration might be how you intend to use it. If you think you need power up to 12x, yet, most of your shooting will be offhand shots around 25-30 yards, you might be heading in the wrong direction. To my way of thinking, getting the best 3-9x scope you can afford is a safe bet. For the price, the Vortex Crossfires seem really nice, Bushnell 3200s are too, but a little more money. I've put some pretty low-end scopes on rimfires and airguns over the years an most of them have over-delivered for their price point. Granted, I never hunted with them in the rain, or subjected them to harsh environments/temperatures. I have a $100 Bushnell Trophy 3-9x on one of my .22s...going on 10+ years. It's been through hell and back, won't die though. Haven't even needed to adjust it in more than 6 years. I have nicer scopes on all my other rifles, making me LESS likely to use that one now, so it might be upgraded just because.
Most 10/22s aren't really range/target guns, so you have lots of options open to you that will work well, and not cost too much.