Well I'm not a dad yet but I'm a son who has been handed-down several rifles.
Among my favorites are a Browning BL-22, a ruger M77 6mm, a Winchester model 37 red letter 12 ga., and a Marlin 336 .35 rem.
I guess if I had to pick a favorite it would be the Marlin 336, since I'm the 3rd generation to deer hunt with it.
But as far as going out and buying a new "first rifle" for a kid that will become an heirloom, I'd suggest a lever action .22lr like the Browning my dad got for me. I've had a lot of fun over the years with that rifle, many a squirrel, rabbit, and tin can have fell victim to it.
The Henry golden boy is a nice looking rifle, but slightly over-rated IMO. The Marlin golden 39A is a nice rifle, but the Browning BL-22 is my fave. I could be slightly biased though
