On your .32 Rem it looks like the rear stock has been replaced at some point. The carbine came with a straight grip stock (no pistol grip). Since this is a family heirloom and you do not plan on selling it I would have it drilled and tapped so you can mount the scope on it. Do you have ammo? As you know this caliber is long discontined and ammo is very tough to find. You can find some every once inawhile at a gunshow or a hole in the wall gunshop. I bought a custom die from RCBS over 30 years ago so I could reload for mine. They are great rifles and if you do reload you can shoot pointed bullets out of it due to the design of the tubular magazine that keeps the bullets from touching when it's loaded. Good Luck with it.
NRA Life Member