Just went through this for the youth compact.243 I bought to get my kids started. Decided on a Leupold freedom 2-7x33 duplex.
Reasons I choose it were;
Long eye relief with big “sweet spot” that seems to be a little more forgiving if they don’t get their face on the same spot on the stock than some of the cheaper imported scopes that I had my 10year old daughter try to look through.
wide field of view,
Smaller diameter so I could mount it extra low for their smaller face and neck
At least for starting them I think 7x is plenty for the max range I will impose on their shot distances.
And I think a lower end “high power” is desired so that if they turned up the power ring it wasn’t going to be on 20x and have a small field of view and they couldn’t find animal. Had a friend who’s son did that on their first hunt and the pig walked away and his kid never saw it in the scope. Later he saw his son had cranked up the magnification to 18x because that’s what he shot it with off a bench the day before.
I went with Leupold because I plan on this being the starter rifle for all four of my kids and possibly my nephews so I was willing to spend a little more for quality and a warranty than if it was for just a few seasons for one kid to out grow.
That said if I had seen a good deal on a quality fixed 4x I would have grabbed one but I couldn’t find any in stock when I was buying it a few months ago.
Good luck