Heirloom certainly indicates something made well enough to be passed down, but I think it needs a little mystique, something that invites conversation like " Oh, Dad must be serious, He just pulled out the Winchester/Browning/Remington etc.. Tree Rat special! " Hopefully it has some special beauty to it, Fine wood, engraving, commemorative badge, or just so different, people want to know what it is! Aka - a commemorative lever gun, a Mannlicher full length stock, a Martini-Henry falling block, Military training rifle (a lot of cool ones out there ), genuine sporter rimfires, meant for adult physiques.
I love the older 39a, especially with the octagon barrel.
Browning BLR22 with an oil finish, due to the short lever throw, but the buttstock junction is easy to break!
Browning BPR22 - BAR22
Ruger international series (if you want a 10/22, this is it ) the 10/77 is kinda sexy too.
Remington (detachable magazine ) 541S or 541T, or ditto on the 552 Speedmaster (oil finish please)
Remington 513t
Winchester 52, 75 bolt action
Winchester 63 semi-auto
Holy grail of military trainers - Springfield 03 22lr .
H&R 65 Reising semi-auto, I dug the green phosphate finish.
Henry Yellow Boy
Martini-Henry single shot target guns are cool.
Weatherby Mark XXII, gorgeous, wished I'd never sold mine.
CZ 452 MANNLICHER
Anschutz 54 or 64 sporters, beautiful, very accurate $$$$
Kimber 82 $$$
Cooper $$$
Thompson Center Contender - short, elegant, accurate and can be converted to other calibers (almost impossible to open for youngsters and some adults) now, they are easily over 500 bucks!
Good luck, let's see it when you get it.