This is the main reason I spend a portion of my practice time learning scales... a little scale knowledge can lead to a lot of improvisation.
I play mine everyday and it's still stock... I'm still amazed at how good it sounds for such a cheap guitar.
I had a thin U neck on an ESP... it was practically a rectangle. :)
I really am an old fart... funny though that I burned out on MTV when I was about 24 too... that was in 1986. :)
Take a look at Maestro (by Gibson) short scale mini-V - These are fun.If your child is too big for that you may want to look at a 3/4 scale like a Dea...