You can keep your 3+ minute groups(although thats pretty good for open sights) and i will stick to my 0.5 minute ones(off a bipod or some sort of rest) or whatever the rifle can do. An accurate .22 with a scope is good out to 100m, you can use it just as easily when spotlighting and have the target and sights in focus at the same time. Open sights are fine to learn with, but IMO you should use the most accurate setup you can when shooting animals. Learning with a scope also helps you see how unstable you hold is, which allows you to practice fairly well without having to shoot. With open sights subtle movement like this is very hard to notice. I would admit i learnt with both types of sights and actually used to prefer open sights (although i cant remember why).
I have used a range of scopes and tascos are fine, Leupold scopes are much better and the really expenisve ones are much better again.