My wife has killed two caribou with 80 gr TTSX bullets out of her .243. I think bullet technology has really increased the lethality of light recoiling cartridges like this.
No personal experience with them, but the Howa mini action rifles in 6mm ARC are very interesting looking for a youth rifle.
My wife shoots a .243 and I think it's the noise that bothers her more than the recoil.