Not sure of the age of your son, but if it helps, I'll go through what I've done with my son. I bought my son a Cricket rifle when he was 5. Single shot, super safe with the "daddy button/cocker," small, and it turned out to be very accurate. I still grab it if I've got a squirrel to dispatch, it hits right where I need it to hit...
When he got a couple of years older, I gave him a CZ 452 Scout that I had bought when he was new born. Excellent quality rifle, and super accurate. It comes with a single shot mag plug, and that works great when you are training a young guy on trigger disipline, safety, and making sure they understand and appreciate taking accurate shots. I think that's a very important part to learning how to shoot. After I felt he had that part down, I gave him a 5 and 10 shot magazine to use... After a year like that, and I was sure he "got" shooting with the iron sights, I bought him a Leoupold scope for the rifle; he loves it.
He's 10 now, and I'm probably going to drag out the Ruger 10-22 that I bought new when he was born. It's been sitting in the safe waiting for him to get older.
Once he gets that down, when he turns 12, I'll drag out and give him the NIB Winchester 9422 that I bought for him when he was a baby. He should be a pretty good shot by then, and should appreciate it!
After that, we'll see what kind of revolvers he's interested in. He's got a pre model 34 that I've given him, but I only let him shoot it when I'm sitting with/hovering over him while firing. Handguns are a whole other level of safety concerns with kids...!
Have fun, and I'd recommend a single shot to begin with...