Well, what does he usually like to use a computer for is the main thing.
And , secondly, what's the Budget that you're looking into?
Are there any preferences in make, region of purchase, screen size , peripherals in the box etc etc.
^ or not... A teenage boy will want to play some games.
That is why I suggest a laptop with a discrete graphics card. You can find some around that will play modern games (at low details, but fluidly) for pretty cheap.
For example, the one I showed can play crysis @1024x768 low details @ ~60fps
Point is that it CAN play games. It totally smokes the HD3000.