That Thompson Center single-shot looks like a sweet little gun for a youngster.
Depends what you are going to do. For sitting at the range and learning the basics of shooting I like the 10/22. A single shot is distracting when trying to learn to shoot.
However, I wouldn’t give a child a semi-auto to a brand new hunter. I used to hunt rabbits and squirrels with a Winchester lever action .22, great fun.
The New England Arms single shots are also great starter rifles.
+1 got one of these for my daughter and she loves it. Has a big peep sight in the back so target acquisition is easy. Nice little rifle. And, she likes it because it looks like daddy’s .308 encore, except daddy’s rifle isn’t pink. Started her off with cheap Remington subsonic. Very pleased overall