Learned to shoot at 6 with a Winchester Model 61, which I still have. When I was around eight I was allowed 1 shell at a time and could handle it myself. At 10 I was given am Iver Johnson 12ga Single Barrel that was pure punishment. "Graduated" to a Winchester Model 12 (which I also still have) and at 12 received my first centerfire, a Remington Model 14 in .35 Remington (also one that I still have).
I've started my children a bit differently, I bought a Remington 1100 Sporting in 28ga to instroduce wingshooting, and they get to start .22 on my Win 61 and a Marlin 2000.
I've laid in a starter set for each child of a Russian SKS, an AR-15, a CZ-52, a Steyr-GB, a Ruger .22 Pistol, a Winchester Model 12, a Remington Model 14/141, a Steyr Scout and a Browning Auto .22. They also will each get a Class-III from my stuff when they are old enough, though not all will get the same.
I may be saddling them with my preconceived ideas in firearms, but even if I would predecease them I'll know that they were each affored the opportunity to start with good stuff.