I'm also throwing in a chip on .243
You know he's gonna want hunt with his first rifle, and he may want more than rabbit.
I don't know texas' hunting regs. Here we can hunt deer with 22, some places you cant. Maybe you don't want his first hunt ruined with sub-optimal shot placement on a caliber that requires absolute precision on shot placement for success- maybe you do.
He's gonna be all jitters on that first game shot- and I know on mine I wished I'd had a bullet the size of my head. I lucked out and got what ended up being a passable single lung, out the other side on the neckish area shot. It was a 30 caliber bullet, not sure that mattered. I'm glad it expanded, cuz that deer RAN, and I can't imagine what it would've been without a well made , big bullet.
You can go from squirrel to deer pretty easily based on bullet and charge with a .243, something else you'll also get to teach him along the way.
With that said, old rifles, and old reloading kit are cool... But vintage is not everyones bag of tricks, and I'm certain you could steer him into a standard marketing stream like Hornady, or RCBS, and let him make his own choices.
If he's earned the right to hold one, giving him the choice on what to hold- and all that entails, requires, and possibly limits, isn't that far fetched.