Hello HuntingGuy,
For a 22 rifle I prefer an objective no larger than 32mm. You will see a lot of people putting 40mm and 50mm on a 22 rifle. I dont like this because it puts the center of the cross hairs so far above the center of the bore. A ½ inch or an inch makes a big difference when shooting small animals like squirrels and rabbits.
People may like the large objective lens because they like to shoot animals 50, 60 or even 100 yards. It has never made much sense to me to shoot a squirrel or rabbit at a long distance away then have to disturb the hunting woods while making your way to claim your animal. If I shoot a small animal that far off and take my time hunting while getting there I usually cannot find them.
I prefer a good name scope like daddy was talking about but if you arent willing to spend a large amount of money on a scope, Swift makes a great scope in the 100 dollar range and they have an over the counter trade in if the scope breaks. I have a Swift on one of my 22s and its very clear and rugged and holds its zero. For a 22, I feel thats all you need. I would look into the 2-7x32 or smaller objective or fixed 4 power scopes and look at several sets of scope rings and find the set that allows you to mount the scope as low as possible with out the objective touching the barrel.
Hope this helps,
Scott