I guess I might be a little old fashioned, but I prefer straight 4X scopes on my 22s. I currently have a Weaver Classic Rimfire 4X on my 10/22 and really like it. It's clear, bright, and designed for rimfire distances, and was just over $200 IIRC. They also make a 2X7 model, which would also be a good choice. Your budget allows for a good quality rimfire scope, so I would stick to known quality brand names.