The .30-30 is a great choice, as are the others. A levergun makes shooting fun, and personally, I'd choose a Marlin, a Win 94 Angle Eject, or a Mossberg so that you can mount a scope and wring out the most accuracy possible for hunting or comparing handloads. Shooting with iron sights is fun too. Of course, there are also .30-30 rifles to be had as singles, bolts and pumps.
It's also an easy cartridge to handload for and you can often get free, once-fired brass at ranges because lots of non-handloaders will leave their brass behind.
As to barrel life? A properly cleaned, non-abused rifle will last you and your son many thousands of rounds. The same applies for the .30-06 or the .308; hunting-rifle accuracy, say 1 to 2 MOA, may drop off a tiny bit after a few thousand rounds, but not critically. That would open up more action types to you if that is a concern.
One other alternative, but one that may be expensive to shoot until you do begin to handload, is the .300 Savage. A bit more recoil and considerably more power than the .30-30, lots of handloading options and data, and will cover game up to moose. Available used in the Savage 99 lever and many bolt, pump and autoloading rifles. Currently available new in Savage bolt rifles. It's a bit of an enthusiast's cartridge because few guns are chambered in it these days, but all the big ammo companies produce it and will continue to do so because there are probably between half a million and a million guns out there in that chambering.