I have to agree with the previous posts; there will be something special about passing down "Grandpa's Rifle" to the person of your choice one day. I don't think it would be nearly as "special" to hand down the gun previously known as grandpa's gun. I agree the -06 isn't too sexy, but you can't complain about its usefulness either.
I have a similar but different situation. I inherited and old single-shot bolt action 11mm Mauser from my wife's grandfather (it was a lamp post when I got it). I cleaned it up and was looking for some ammo, I thought it would be fun to shoot a deer with this old gun. But then I remembered grandpa was a non-hunter (not anti) just didn't want to kill the preaty animals himself. Since I figure he may not have wanted to be involved in hunting I decided to shelf the hunting idea and will some day see about busting rocks with it. SHould be interesting using the old ladder sight way out there.
Genises 27-3: Now therefore take, I pray thee, thy weapons, thy quiver and thy bow, and go out to the field, and take me some venison...