I missed this thread the first time around as I was gone for some training. But wanted to comment now.
I like the idea of starting a youth out with a rifle they can be proud of and something they can carry and eventually pass to their kids if they choose to. The downside to that is #1 the price and #2 there will be bumps and bruises to the rifle as part of learning how to handle a rifle.
I like the Remington model 7 and I like the Ruger 77 compacts. Anything in the .243, 7mm-08, .308 range would be fine . Twelve year olds aren't all built the same. At twelve I was shooting 12 gauges and .30-06s. although my deer rifle options were a .44 mag or a .30-30 lever. But some kids are more recoil sensitive than others .
Proper fit and proper form are very important.
Here's two Rugers and a model 7
-Jake