For a 12-year old, I would consider calibers with a relatively moderate recoil (as others have stated). Look at the 260 Remington or the 7mm-08 - they are almost identical in performance and have very manageable recoil.

Since I'm not able to get a new rifle for my own 12-year old this year, I am having him shoot my 30-06 using Remington's Managed Recoil ammo. We've been to the range and he went through a box of this ammo without flinching once.

Take a look at this page for some info on recoil: http://www.chuckhawks.com/recoil_table.htm The numbers may not be perfect, but I think they give a relatively good idea.

As far as brands go, I think there are a number of good options, including the economical youth models from Savage. I have heard some very nice things about Savage's AccuTrigger, and that might be enough of a reason to give 'em a look.

I like bolt action guns, especially for my son. They're reliable and slow to cycle the action.

Rossi Arms also has some combinations where you can get a rifle/shotgun setup (interchangeable barrels)for under $200. A 20 guage/.308 combo might be just the ticket...

Braveheart1621 mentioned a 270. The 270 is a fantastic round, but I wouln't get one for my 12-year old. It's a necked down 30-06 so it still pack about the same amount of recoil. The 7mm-08 is a necked down .308, which has milder recoilto begin with. Just my thoughts.