I will throw in and agree with what everyone has said.  My son is eleven (will be 12 Oct. 9 so we have to wait until the 9th to get at some big game), but we started him out at 9 I think with the .22 in 4-H, BB guns before that a little.  It was just a timing thing, there are 8 year old in it I think.  We had to go through the hunter safety and everything to shoot 4-H.  I think it is a good program to get them into, plus doing stuff on your own with  them.  6 might be a little young for hunter safety, but like Hilltop said, it depends on the kid.   I am thinking of auditing hunter safety again for ours, just because.  Grandpa kindof spoiled him with a pretty nice .22, but those cricket ones are pretty good.  I have had my remington pump .22 since about that age and it is still pretty fun and shoots fine.  Those single shot ones are also a good idea to teach shooting mechanics and probably a little safer than the pumps.  I used to get all Lucas McCain with that thing, it was pretty fun.