Kicker, another vote for the 7mm-08!!!!
I own a .280 rem and my wife shoots a 7mm-08. I load for both. I can get 200+ fps more out of the .280, but at the cost more recoil. And the .280 is ported. Personally, I love the .280. But for a 120 lbs woman, or child, the reduced recoil of the 7mm-08 makes them much more dangerous since the recoil is so manageable.
I've never measured recoil like this Hawk guy but just look at any reloading manual and the 7mm-08 has about 15% less case capacity. Powder means noise and recoil. Some calibers are just inhertantly more efficient. And I believe the 7mm-08 with a 120-140 gr bullet is the perfect bullet for a new shooter.
I load 139 gr Hornady SSTs for deer and antelope, 140 gr Barnes TSXs for elk. Her rifle has dropped 2 elk in their tracks between 180-200 yards. She did lose one but she shot it too far back on a running shot which, in hindsight, I should have told her not to take. But a running animal, in timber, she'd shot before i really could have said anything.
I use the .280 as a comparision since it is so close to the .270 win. For your application I swear by the 7mm-08.
Other calibers I would consider would be the .243, 257 Roberts or .260 Rem, maybe even the 25/06. But IMO the 7mm-08 is a lot better all around caliber if elk or moose are a possibility. If anything bigger than deer are 4 or more years in the future, the .243 would be my choice as long as you are willing to buy another gun for him in 3-4 years.