Myself, I'd start with your hold with that 10/22.
If your cheek sits low on the stock the scopes with a large bell (high ring/high mount) are out. You'll be long necking/upright/pulling your head off the stock to shoot.
Too short of a scope and you could end up crawling the stock to see out of your scope.
What is most of your shooting going to be??? Huge difference between a scope setup to shoot bugholes and a scope for hunting.
Will the majority of your shooting be done from a bench, standing, sticks,etc???
A ruger 1022 setup for silhouettes, long bodied scope with the rear of the scope set back well over the handgrip. High cheek rest/cheek a short bodied scope will not be able to do this. A 8-32 x 56 scope with thick to fine crosshairs.
With a lower stock I like to use scopes with smaller bells. A lyman 20x on a field stock that's setup for offhand shooting. Again the long bodied scope is set back over the grip. That scope actually is an excellent choice for the cx lux's, the long body clears the rear sight and is still long enough to go back far enough so that the shooter doesn't have to crawl the stock when shooting offhand. 20x dot reticle
A anscutz fs setup for sitting/squirrel hunting. The rear of the scope is forward compared to the offhand setups pictured above. A 4x with a post reticle.
Another squirrel rifle, a Remington 513s setup for woods walking offhand hunting. A 3-9 x32 with thick to fine crosshairs
Years ago 4p shooter used sliding scopes for the different positions. I've sold off my 40x's and 52'd but I still keep a x-series Anschutz 54 (still nib) around just in case. I've also sold off my feckers & unertl's but I still keep a cheap tasco (made in japan) around. The tasco sits on a rem 540x setup for offhand.
The Remington 540 series rifles have the fastest lock times of any rimfire rifle they ever produced. I like to take a 22lr rifle with me to the range and play around shooting offhand between sets/bbl cooling/etc. I find it relaxing, typical 5-shot groups @ 25yds with that 540x/tasco scope pictured above with blammo ammo from Walmart.
If you can't find anything new that appeals to you might consider looking at the older scopes made in japan from the 60's/70's/80's. Excellent value for what they are. A 4-12x40 bushnell scope with a bdc and thick to fine crosshairs that I use for standing silhouettes/modified taco hold.
Anyone can buy a scope, why not buy 1 that that is right for your style of shooting. A jack of all trades is a master of none and scopes are no exception.