^^ this... why this perfect option is uncommon and rarely made anymore is a sad testament to the marketed "need" for a product that boasts nothing new.
I grew up being recoil sensitive because I shot what we had (therefore was in budget) and got beat up: Every new shooter I have taught enjoys calibers appropriate and I'll shoot the heavier guns so they get the chance to observe the increased recoil... until they grow or experience is gained. Charles Newton ticked all the boxes back in 1915 in his cartridge design for Savage's 99 and has yet to be topped by whatever the information age can muster.
Flinch plagued me for years and took a long time to beat: I see no value in failing to pass on that lesson.
Off the shelf, a modest budget and with abundant supply of factory ammunition I'd just opt for the 7mm-08. Personally, a model Seven in 250Sav would make an optimum package for a young hunter for <500lb game. (Take it and run Remington... that niche is currently unfilled except by the high end Cooper. It'd cost nothing reverting to production of timeless classics, but marketing the latest ...)