I know what you mean about having to much power and the limited field of view to rapidly pickup a target. I recently bought a Leupold 2x7x28 VX-1 rimfire scope for one of my .22's. It is a nice compact scope and weighs only about 8 ozs. Size wise it looks fitting on a .22 rifle. It costs about $200-220. I am not an advocate of mounting big scopes on .22 hunting rifles. Target rifles yes, hunting rifles no.
My favorite .22 scope is an old Weaver V4.5 which is 1-4.5 power. Set at 1 power it is easy to find a squirrel in a tree and once found the power can be increased. Set at 1 power it is also easy to track a running rabbit. The parallax is not set for .22 ranges, but I have never had a problem getting half inch or less 50 yd groups with my rifles. If I were going to buy another scope specifically for a rabbit/squirrel rifle I would buy the Weaver 1-3x20 ClassicV which is only about $160.
Good luck on your decision making, Jim K