OK, I'll make it simple.
If the goal is to simply spend as much as possible on sealed (over the ear) headphones that an iPod can power, then the answer is the Audio Technicas that were already mentioned (model M50). I have these on right now. A 12 year old probably wants bass. For sealed cans this is probably the way to go as these have a better low end than the Senn HD-280s and most other headphones in this category. Where category is defined as
(1) Under $200,
(2) for a kid (more basss is
typically good to a kid),
(3) over the ear (sealed) and
(4) powered by an iPod.
You know more than alot of people.
If you want to spend less, the Senn HD 280s are an alternative.
The other bottom line is that without knowing exactly what this kid listens to, there is no way to recommend anything perfectly? The Audio Technica M50s are pretty much it in my opinion.
The nest step in sound quality would be to get a headroom BitHead which is a $150 headphone amp.
http://www.headphone.com/headphone-amps/amplifiers/headroom-total-bithead.php
The Airhead which would also work is $100.
You could try coupling the airhead with a lower cost pair of headphoens that need a dedicated amplifier. Probably not for a 12 year old unless he is an erd like us (likes engineering, etc)