Well, I'm in my 40s so for me the biggest scope I can get is better
I think the one I've got on my Yugo rifle is something like (mine is many years older)
this
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That is a 6-24x 44mm objective. As a cheaper scope (ie, not a $1200 nightforce) the edges of the fov are a little blurry. Seems to deal with recoil OK, but not an issue for your use.
Bigger bell will require higher rings but let in more light. Get a weaver/pictatinny rail for the 10/22 and mount to that - the stock dovetail rail likes to shoot loose. There are some companies making rings that mount right on the receiver, but I've got no experience with them. In theory, one less interface means a stronger joint... but theory sometimes doesn't mean jack.
The 4x power I have permanently on my 10/22 is maybe 32, 25mm objective? Don't recall. Works fine though. Go for something that looks like a traditional rifle scope though, and not a small tube 'tactical' type. Less light transmission among other things.