How tall is he and how much does he weigh? What rifles has he shot before? Do you know if he is recoil sensitive or not?
A youth 243 Win or 7mm-08 Rem would be my choice. Which of them I'd choose for him would depend on what he can handle in recoil. If he can handle it properly, the 7mm-08 is a fantastic choice, completely capable of taking bull elk at reasonable ranges, with the proper bullet!
As far as rifles go, the Ruger American rifles are my first choice, followed closely by the Tikka T3X. Ruger makes their American rifle in a Predator version called "Ruger American Go Wild" camouflage in 7mm-08 Rem that has a little heavier threaded barrel and come with both a 5/8"x24 TPI radial muzzle brake and a 0 MOA Picatinny rail already installed. They are superbly accurate (sub-MOA) and can be had for @ $500 shipped from Bud's, G4Gguns and others.
The Ruger American Standard rifle can be had in a 243 Win youth model that is very light weight and also shoots sub-MOA. Unfortunately, it is not available with the threaded muzzle. Most of the Ruger American rifles have some left-hand version available. They are currently running around $370.