Personally, I think that is a choice you have to make based on experience. I started with a Crossman 1377 that my dad bought me as my first BB gun back in 1978, I was 5 years old. My dad spent a lot of time training me about firearm safety. We had various 22 rim fires and other firearms that I would shoot with him.
For Christmas, in 1983, I got my first 410 single shot shotgun. I was 10 and was very safe and allowed to take it out and shoot by myself. At 12, I got my first rifle, a Ruger 10/22 with a 25 round mag. By the time I had turned 14, I was shooting 12ga shotguns, .308's, 7mm, and had my own Barrett 9mm pistol, and was free to come home from school, grab any of them and head into the woods and hunt, by myself at will.
so I guess what I am saying is, it all come down to experience, knowledge, and maturity level as to what you hand them as a first weapon.