I started when I was about 12. I had been shooting firearms since I was 6 (a .22 rifle under supervision obviously!) When I started shotgun shooting it was with a Remington 1100 12ga. I was big for my age, but the gun still didn't come close to fitting. I was given instruction on the operation of the gun, specific safety rules of the sport, and how a round of trap runs. When we got to the range it was empty and the trap machine was stopped from moving and we shot straight away targets then progressed to all the angles a trap machine will throw. I have seen kids as young as 9 shooting, I think it depends on the maturity of the kid. The only kid that had his parent directly behind him was 14 and he needed the supervision. The 9 year old was very safe and no one even thought twice about him not having his father right behind him. In reality Trap is a VERY safe game. On shell loaded on shell fired. Gun's always pointed down range.
As for what to consider. It's all about maturity. Does the child act responsibly? I think starting a kid with skeet or trap makes the most sense until they build their shooting skills a bit. The one thing that I wished happened differently with me was that I would have liked to start with a smaller better fitting gun. I got BEAT UP! My whole upper body hurt terribly for a couple days after each trip to the range. I still enjoyed it enough to keep shooting but it made it less fun and harder to improve.
As for what to consider. It's all about maturity. Does the child act responsibly? I think starting a kid with skeet or trap makes the most sense until they build their shooting skills a bit. The one thing that I wished happened differently with me was that I would have liked to start with a smaller better fitting gun. I got BEAT UP! My whole upper body hurt terribly for a couple days after each trip to the range. I still enjoyed it enough to keep shooting but it made it less fun and harder to improve.