I wouldn't look past 7mm-08 either. The reduced recoil rounds kick about the same or less than .223 and you can go up to heavier bullets down the road. Both of my kids got these at 12 and I really like the round and how it performs.
While it may be objectively untrue, I was going by the comments of my small statured 12 year old.That is objectively untrue (unless we're talking about very different rifle weights). Both from personal experience, and the fact that even reduced recoil 120 grain bullets going 2500± will absolutely generate more recoil than a 77 at 2700±.
Going from a 7mm-08 to .223 and 6mm ARC rifles is the best thing I've done for my kids' shooting.