I have three sons, with one still at home. I started them on BB/Pellet guns very young. With the introduction to BB guns, also came the introduction to gun safety. Gun safety has been drilled into their heads over and over again. We moved from BB guns to 22s and so on.
I think if you are going to have your kids around guns and eventually teach them to shoot you must start them early. As far as what age to let them shoot the "big guns", I think that's a judgement call made by the responsible parent being able to recognize when they can handle it.
This method may be controversial and not the way the know-it-alls do it but that's the way I was taught so that's the way I did it. I got my first gun, which I still have, at 9 years old...a .410 single shot and was dove hunting with my dad and granddaddy at that age (well supervised, of course).