I have grandkids in that age range...and from 2 to 25.../ and every kid is different....some of them want to start shooting around 8 or so --- but it comes down to attention span and how much they want to do it - and do they have the arm strength to point a weapon.
Some kids are ok around 8 --- but for most of them, its closer to about 11 or 12 ...( and I have both boys and girls )....
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As far as guns .... a model 18 S&W 4" revolver has worked very well / the model 617 in a 6" proved to be too heavy. So if you go with a revolver...weight is a factor.
In semi-auto .22's.... Browning Buckmark was my choice ...and its been a solid gun for them to learn on, learn how to load the mag, etc...
As they get a little older....conversion kits on 1911's or on Sig Sauers...in .22 have worked out well...
and around 14 or 15 yrs old ...as I transition them into a 9mm...keep the guns on the small side, lighter and single stack ( Sig 239's worked out well, I have a Kimber 1911 4" alloy frame Tactical Pro model in 9mm as well...and keep the loads "light" and you'll be ok ).
Most of the .380's were too difficult to rach or operate because of stiffer springs in many of them ...so I took them from .22's to the Sig 239 or the Kimber 4" in 9mm...
At about 16 --- they transitioned into heavier calibers..and heavier guns ...but many kids still have smaller hands ( so stay single stack )...but K, L or N frame S&W revolvers, I have a Freedom Arms single action ( all in .357 Mag or let them shoot .38 spl's in them too ).....leave .40 S&W, .45 acp , .357Mag or .44 mag for the older kids - 16 and up...
and let them have fun !! ....pick cool targets, some simple games ( like Tic Tac Toe ...) stuff like that...