Another thing about the 308 is you won't need a long barrel to burn up the powder, which makes an easier handling rifle for small framed people.

When I was growing up my grandfather sporterized Mauser98s. His favorite lower recoil starter cartridge, and the one I started out with, was 250Savage (250/3000). He also built many 300 Savages. I killed all my deer with either a 250 or 300 Savage.

If I was starting out a kid today it would definitely be a .243. I love that cartridge. 6mm is great for Texas whitetail, coyote, pigs- whatever.

When they get used to the 6mm you move them over to a .308.

I wrestled with the same question, but came up with a slightly different answer for my 15 year old and 12 year old boys:
a Howa Lightning 1500 in 6.5x55 swedish mauser. The 6.5 is a mild recoiler, yet has a very good reputation on deer sized game. Once I get it dialed in accuracy wise (a little disappointing thus far, am hoping it will improve after glass bedding the action) I would not be afraid to load some 140 gr Nosler Partitions and use it on elk, at ranges under 200 yards, I think it could do the job. Its' recoil isn't that much more than a .243 with 100 gr bullets, and the price was right.

You have two good choices in mind. For a nonreloader, 308 would be hard to beat. For someone interested in getting into reloading, I might consider the venerable 7X57, it is a classy old gal in her own right.

I'll second the 308 and light loads, with honerable mentions of the 7x57, the 7-08, 260, and the 6.5x55.

Across the board, taking into consideration recoil, rifle balance, muzzle blast, etc, the 25WSSM in a Browning might just be the ideal new gun for a beginner.

I believe that so strongly, I bought my kid a 270... It doesn't make that much of a difference. LOL! Dutch.

Non-handloader: .308 Win; speaks for itself
Handloader: 6.5X55 SE; as mentioned above, great potential with high SD 140 grain bullets, generally very accurate, manageable recoil, great versatility to the handloader (light 95 grain loads up to full house 140/160 grain loads). The 7X57 is a viable option too, and allows for slightly heavier bullets for elk.