It's so cool to see a mother do something like this for her kid. Definitely admirable. And brave; the internet is a dangerous place.
I'm not too familiar with the GBA/GC connecting, not owning a GBA myself, but the others seemed to have put it rather well. Stick with official products, definitely. Also, I highly recommend Four Swords (it's a Gamecube game and can use a controller, but for multiplayer you need two to four GBAs). I've only played single player and it was fun, so if your kid has friends with GBAs it should be a total blast. You'll need all the connection cords, of course.
I suppose I'll let you do your own shopping.

Just, if it's convenient and possible, Four Swords is a really fun game.