RL,
Pistol....I would go with the Ruger MK II. (Like the one in the Pic)
Rifle.....I would go with this one
Link
I have a Ruger 10/22 and I WOULD recommend it to most shooters but for beginners I recommend a bolt action because it teachs patients and the importance of single round hits. Kids (and some adults) lose sight of this when shooting a semi-auto rifle because of how easy it is to do follow up shots.
Also you might want to pick up an Air Rifle recoil is near the same as the .22 but if the kid starts flinching because of the noise you can put them on the Air Rifle.....same line of thinking as ball and dummy drills.
HTH