You're spending some time thinking about it, and reasoning through alternatives. You'll do great.
Whatever you choose, you'll have some very sweet time together.
My granddaughters were afraid of the rifle to begin with. But as they learned to handle, aim and fire it, they quickly gained confidence. Learning that they can do scary things is extremely important.
Grandsons really like the 10-22, but they treat it like a video game, and see how many shots they can get off. The objective seems to be to blow through as much ammo as possible, rather than develop skills. The girls seem to do much better at that age.
My grandkids love my Henry lever action rifle. You might also look at the CZ452 bolt action rifle. It's very accurate and well made. Their starter model has a stock that is a bit short, but not too short for an adult. It comes with a block the fits into the magazine well, making it a single shot. But you can replace that with a magazine later.
If you do choose a semi-auto, the advice to only give them a single cartridge at a time is very good advice for the first while. At our range, we had a father give his son with zero experience a 45 with a full magazine. The kid popped off the first round, the recoil brought the muzzle back under his chin, and he pulled the trigger again. Miraculously, he survived with only minimal issues. It was the first and only serious injury the range has had in 25-30 years of operation. But the point is, if the father had followed the advice others have given here, the accident would never have happened.