A fixed power scope of 4x will do anything you'll ever need to do that the winchester 190 rifle will. The MAIN thing to do tho is get a scope that specifically for .22 or airgun. Otherwise,the parallax is going to be set for too long of a distance,100-150 yards. You cannot change parallax yourself. You can however adjust the objective lens to compensate,in a model that features adjustable objective lens-usually in the higher magnification models.
In other words-stick to .22/airgun scope. That don't mean you have to get a lower quality scope,in fact it has nothing to do with quality.
A basic 3-9x40mmAO would be good IMO. My quick grab varmint supression 10/22 usually stays on 6x and 50yd objective setting. POI is the same for 25 or 50yd with my 22lr. IMO, the 40mm objective is better simply for shooting in lower light conditions. I use AO (adjustable objective) scopes on both of my 10/22's as I also use them for silhouette matches ocassionally. My heavy sports a 4-16x40AO scope. Both have target turrets. The Simmons were aftermarket, the BSA was integral. The BSA scope is however 1/8" clicks......I always have to remember that!