Okay, so I've been working on this a bit. I love GURPS, but I stopped using it for this. While I wanted some mechanics in my kids' first RPG, GURPS was just too much. For one thing, the mechanics were more rigid that I wanted, and I felt that by throwing out so much of the rules and home ruling so much, I was probably just using the wrong system.
We've been looking at Spirit of the Century lately. While my group seems lukewarm on actually playing it, I really liked the FATE system. However, I wasn't sure about the use of Aspects and how that would go over in an introductory game. So, I back tracked a little bit and investigated Fudge, the basis for FATE.
I remember when Fudge was being developed and kind of kicked myself for not really looking at it until now. I like the system-- although it's probably fairer to call in a framework than a complete system. Not being given any Attributes to start, three different combat systems, two different character creations systems-- it's is kind of daunting. I can see how FATE developed out of it, especially given articles like this and this from Fred Hicks.
Anyway, I found a guy, Knaight, on the Fudge Forums, who already had an aborted attempt to translate Pokemon into Fudge. You can see most of my work and his comments in this thread. He had obviously already put some thought into the translation, and his comments have really helped me out. I'd say right now, it's just about ready to run. I think the combat really captures the flavor of the games (which my kids have played a fair bit of), although it might be a little too complicated still. I'll have to work a bit more on it. I will possibly add FATE points and develop the characters via Aspects...we'll see.
I found some Pokemon CCG League badges-- real pins you can put on your clothes-- cheap on eBay. Once the kids beat a trainer in the game, I will give them each a real badge to wear! What a prop! I think they'll be impressed.
I also picked up some mics and a mixer, and will take a stab at recording the games. I don't know if I'll post it, but I think it would be kind of cool to have your first RPG campaign you ever played recorded!