Let's admit it, we buy guns for ourselves(youngsters).
In your choices, if you pick a firearm that may have a cheap aftermarket plastic stock that you could cut off, then as they grow, you could put the regular stock back on.
Remember that old trick on establishing the Length of Pull a person needs? Bend your trigger finger, and measure from the bent index finger to the crease in the arm, inside the elbow. This distance on children is between 10" to 12" as a rule.
If the stock is too long, they will not be able to get into the eye box of the scope, NOR will they be able to reach the trigger. They will have to let the stock ride under their shoulder in the armpit. When the trigger is pulled, the scope may cut their face to the bone or they are scared it will on some centerfire cartridges.
In our family, Great Grandpa, dad, and uncles always got the kids their first centerfire when they were 14, safety and gun fit. There are some guns such as Thompson Contenders that make fantastic rifles for youngsters due to their lack of weight in the forearm and weight not to mention the plastic stocks that are available.
Remember for youngsters, a 4.5 lb trigger pull is going to be horrifying. Youngsters need to spend a lot of time practicing with a 22 Long rifle bolt action rifle with scope.
My Great-grandpa got all of us youngsters throwing up Penneys and shooting them with our BB guns, taught great hand and eye coordination. Great Grandpa watched us as he sat on the front porch shooting Carpender bees with his 22 rifle using shorts.