If you’ll pardon the poor quality pictures, a few more suggestions. A Browning SA-22, gets close to that $1,000 you don’t want to spend ($800 new, less used).
Ruger 10/22 Sporter with walnut stock. Not a bad rifle that everyone ought to own at least one of (IMO).
Henry lever. Pretty enough from 10’ away, offered in blued, “brass”, engraved, octagon barrels, etc. They run the gamut from around $400 up.
CZ. Of course I’m gonna chime in with everyone else and add them to the list. A more refined rifle than most at its price point and still reasonably priced.
None of the above is heirloom quality but all of them are quality rifles that will last. My suggestion, tempered by my own thoughts on handing down firearms, is to chose what you want to shoot. Enjoy that rifle, make it yours, and don’t fret over what will become of it once you’re gone. No doubt in my mind a good number of my firearms will be sold off by my children and if that suits them, I’ll still have no regrets over what I bought.
My copy of the Browning SA-22. Light, svelt, nicely finished (the Brownings, this one not so much).
Sure it’s just a 10/22 but it’s nice to own something you can tinker with that is also dead reliable.
Henry makes for a respectable looking lever (this one is a .357 but serves to stand in for the pic).
CZ!!!