Although I own only one bolt rifle (a LH Ruger), I've harvested more deer with borrowed RH bolt guns than with my LH bolt. That said, when I bought my first bolt rifle, I bought a LH bolt.
If you only ever take one shot at an animal (which we all strive to do), there is virtually no difference between a LH and RH bolt. If you take your cheek off the stock to cycle the bolt prior to a second shot, there isn't much difference between a RH and LH bolt. It becomes quite difficult if you shoot LH trying to cycle a RH bolt without lifting your cheek off the stock.
So why should shooters/hunters who are LH, left-eye dominant spend a good deal of money on equipment that will force them into awkward, less than optimal shooting techniques? IMHO, if you have the money to buy a rifle for your son, then buy him one that fits him, not somebody else. If you only have the money to buy one for multiple people to share, then that's a different story.
Semi-autos are another good option. I've never fired a semi-auto that is a problem (Rem 1100, Rem 11-87, M1 Garand, Ruger 10-22).