First off, good on you for raising a son who hunts with you. My kids are just babies, but I daydream quite a bit about getting them out in the field... so even having him shoot a couple times a year and then just hunting is a great accomplishment.
As others have said, ask him if he prefers a specific cartridge. He might surprise you and be more interested in rifles than you think. That said, it seems like the .257 is plenty for deer, antelope, hogs, etc. I know people who hunt black bears with equally or less powerful cartridges. So you've already got him covered for that stuff (which might make needing one rifle that can do everything unnecessary?). Seems like something of the .284 variety would be a good choice. You could pretty much kill any of the same game as an 06, with less recoil, but with enough of a difference in "umpf" to consider it a clear step up from the 257. 708 is more than just a kid's cartridge if you want mainstream, 280 or 7x57 if you want to bridge mainstream and rifle nut territory, or 7x64br if you want something very unique but still utilitarian. You aren't going to find the Brenneke in a M70 FWT, but there are some very cool older Mauser clones out there just begging to be refinished... and that kind of father/son project might be what finally pulls him into the looney realm with you?
