My first 22 hornet got a Weaver 2X-7X, and it was ideal. On my last 22 Hornet, I had a Leupold 2.5X-8X. The magnification was perfect for varmints out to 200 yds. If you decide on another make of scope, the magnification should be in about the same range.
I tend to favor Leupolds, becasue of the excellent quality of the optics. Burris makes a very good scope. Bushnell Elite is also a very good scope. Any of these will run about $400. The new Weavers and Redfields and Simmons Aetec scopes are all made by Meade Instrument and are pretty good and run about $300. Nikon makes a good scope, but stay away from their lower end scopes. They tend to halo really bad at high power.