Actually, think it's a no brainer.
It is if you read the OP's criteria:
*500 yard standard shooting distance (possibly a little farther, but dont really have anywhere to shoot more than 500)
*Manageable recoil. Something a 13yo girl, and 11yo (both with very little rifle experience) could handle
*under $800 without optics (slightly flexible, but prefer to stay under)
*Bolt Action (i just really want a bolt gun)
*Just for target shooting. I dont hunt, nor do i plan to anytime soon
*Easily re-loadable ammo. (I reload for .223 right now)
Manageable recoil for young kids, hunting not in the future, and he already loads for .223.
Unless a Palma match is in his future, no need for .308
Laphroaig