That's cool, K-Man. Looks like you're bringing them along right! 
Shot placement is key, no matter what the caliber, IMO. If you gut shoot a deer with a .300, you still have a gut shot deer to trail and try to find.
My thinking is to get a gun that a kid can shoot accurately first and foremost. That usually means low recoil and a crisp trigger. Teach 'em how to breath and squeeze and keep their head down looking through the scope after the shot. A 4 year old can do that with a BB gun, after a little instruction. Then, when it's time to move up to a .22 and then a centerfire rifle, the skills go with them. At that point, caliber isn't the most important part of the equation.

Shot placement is key, no matter what the caliber, IMO. If you gut shoot a deer with a .300, you still have a gut shot deer to trail and try to find.
My thinking is to get a gun that a kid can shoot accurately first and foremost. That usually means low recoil and a crisp trigger. Teach 'em how to breath and squeeze and keep their head down looking through the scope after the shot. A 4 year old can do that with a BB gun, after a little instruction. Then, when it's time to move up to a .22 and then a centerfire rifle, the skills go with them. At that point, caliber isn't the most important part of the equation.
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