A Mueller APV (~$120) is a pretty decent entry level light-duty scope and is a popular choice with target shooters just starting out in the sport. To the best of my knowledge the only downside for rimfire use is the thick crosshairs but that shouldn't hurt for hunting. My favorite scopes for 10/22s are Weaver V series and RV7 2.5-7x28 and RV9 rimfire scopes and the Leopold VX-1 2-7x28 rimfire scope. The top one has an RV9 3-9x32 Rimfire w/AO and the lower has a V24 6-24x42 w/AO. FWIW Natchez has Weaver V16s and V24s on clearance sale for pretty cheap.
Proud Life Member: National Rifle Association, California Rifle & Pistol Association, and the Second Amendment Foundation.
Annual Member: Revolutionary War Veterans Association (Project Appleseed) and the Madison Society.