Caliber I would be suggesting 243 or 6.5Creedmoor.
7MM08 is a fine caliber and would serve the role well but 6.5Creedmoor I'm almost certain has SLAUGHTERED 7MM08 sales.
I think a Ruger American 243 Youth with Leupold VX3i 3.5-10X40 in Talley mediums you would be hard pressed to do better at the price point.
https://gunprime.com/products/ruger-american-compact-rifle-black-243-win-18in-gl-d504bb-855596562https://www.nwarmory.com/product/le...ft-100-yds-fov-1-tube-black-matte-duplex