I prefer AO on pretty much all my stuff, you may not need AO, but it is an asset most of the time.
While 4x will get the job done, there is nothing better than cranking up the power on a 2-10, 3-12 or 4-16 to see those tiny 22 holes in your target or observing your quarry at distance before poking a hole in it!
It's fun also to watch the bullets trace on the way to the target with some of the higher power settings, or see the goo fly out of the far side of a squirrel!
Big glass and high magnification I prefer! Unless your trying to keep weight down, or have a particular balance problem, the bigger glass will offer so much more fun and usefulness than the lower magnification scopes will.
Don't be afraid to use a scope with a big objective either, the more light, the better for you, and the worse it gets for the vermin rooting in your garden at dusk!
While you don't mention your price cap, the Weaver line is a good place to start. For the money conscience, the 44/40 series is good. Minox is another good one along with Vortex.
So, while you do not absolutely need a big objective, high magnification scope on a 22, if you do use such a animal, it will definitely be to you benefit!