What I have
is a Schmidt and Bender 2.5-10x56 scope on my Anschutz. It's way above your budget. What I would get if I were you is a Leupold Vari-X III 3.5-10x40.
This scope would be great for hunting, as many of your shots would probably at the lower end of the power spectrum. More power than this for hunting maybe would be needed for a centerfire gun. You have a rimfire whose outside range is maybe 175 yards. At 10x a target that is 175 yards away appears 17.5 yards away!! An easy shot, even if you had open sights.
For the money Leupold has it all: Fully multicoated lenses, ruggedness, good adjustment pots, a wide choice of reticles, good quality glass, and a lifetime guarantee. The model I quoted was only $30 over your budget. Go for it!!! You will never regret having good optics.
I agree with Bill A. unless you're shooting from a bench, higher powers are useless.