Reading the 1st post again...
The TRX250EX is just fine for yore kid. Go online to RockymoutainATV or whatever aftermarket accessories catalog you like and order him a matching set (same company) Baja front bumper, nerf bars and rear grab bar (lil mate cooler type), get the twist throttle. Those are easy items and cheap modifications that will allow you time with him, making that quad cooler in his eyes and time spent together building it up.
Next, open that air box up, toss the lid and stick a K&N on it. Pick an exhaust, a slip on is fine or a full system if you wanna spend money - either are more for looks and sound, then actual performance gains on that motor. Based on what set up you choose, you will need to re-jet the card. Go to a slightly smaller profile rear tire (MX Style) and it will feel much snappier.
You can widen the front and rear with wheel spacers, easy, cheap or go big with a Arm extender kit and new rear axle. IMHO wheel spacers are just fine unless your kid wants to go jump every hill he sees, all day long LOL. I've heard TRX300EX shocks and Banshee shocks fit as stock replacements, upgrades on the cheap.
Then you can get into the motor, but just like Rivermobster said...better suspension will build his confidence to use all that motor up to its potential. Too many people hop on a machine with more power then they can handle and get hurt.
This was a good source for allot of questions your asking....
Theres alot of repetitive threads asking the same info over and over again. To cut down on answering the same questions all the time, and differing answers to further confuse everyone, here's a FAQ to clear everything up. To find what you're looking for, simply look below this paragraph, and...
www.atvriders.com