Softest shooting .223 ar

Loose the bull barrel too heavy. If you want this to truly be the lightest recoiling with still being light weight you should do the following:

16" light weight barrel (not SPR and certainly not Bull) middy gas system
Adjustable gas block (JP or Vltor)
MSTN or Cooley Muzzle Break
Either a JP steel LMOS or Young Lightening bolt carrier
Bolt with extra power spring black insert and o-ring
carbine buffer
lightest tube hand guard not covering the GB
Stock UBR is going to be heavier then say the CTR.

Now set the GB so it cycles reliably but not much past that.

The lighter carrier and buffer means less moving mass whihc if only supplies with jsut enough gas means super light recoil. This minimizes the primary recoil. Then the use of the break minimizes the secondary and also muzzle jump. This is how I have been told they set up 3gun ARs and it is to bring recoil to the absolute min to allow the quickest target acquisition possible.
Of all the parts the two most important are the adj GB and break. You also want the lightest buffer you can get as the lighter the less gas needed to cycle the action. This is what Constructor has been slowly nailing into my head when I am smart enough to pay attention. I would not setup a home defense or combat gun this way but for hunting or a young kid training I think its perfect. You can make the gun super light and yet still have super light recoil. Both of these things will allow a younger shooting to shoot longer and not develop bad habits : flinching, leaning backward to brace the weight etc.. They can concentrate fundamentals without distractions and still be using enough gun to take game.

You are correct heavy and slow or light and fast. If you are shooting off a bench then heavy and slow will give more of a slow shove and you have the increased weight but the quickest follow up shots will be with the light and fast. Also don't forget heavy is not used arbitrarily the rifle is going to be heavier whihc I think is a neg for a youth. Check out how all the top 3gun guys setup there systems. In that game its all about fast follow shots and staying on target. Any one that has shot a decked out JP or other setup 3-gun comp rifle will tell you it has the recoil of a .22 LR and it uses the light system.

If you think about it it makes sense with a heavy system you have much heavier mass moving that has to be stopped and the increased weight of the total rifling which also helps of course. With a very light setup in the same system you would normally have only traded one for the other, lost weight, and with the extra speed the timing woudl be off but that is where controlling the gas comes into play. Tune the gas so the light system has just enough to cycle and now you have less moving mass with out a huge increase in bolt velocity and timing is now tuned. Take away being able to tune the gas system or the size of the gas port and heavy makes the most sense as well with a bench gun. But if this is about making a rifle with the least amount of recoil and one that is a light and easy to hold gun then with only a very small amount of extra cost for the Adj GB you can have a rifling that is very low in felt recoil.

Honestly though my 9 yr daughter shoots my 6.8 with my top loads without an issue so unless they are sensitive to recoil or you see them jerking very badly it may not be that big of deal. I certainly would not make this a first rifle for a kid. A single shot .22 LR like a Ruger is a great choice if they are even smaller then they have those really small .22s that are called Peewee IIRC.