Meh, the PSP is great for doing stuff besides playing games, (watching DVDs, surfing the 'net) but if you're going to get a handheld solely for games, the Nintendo DS is better. You think Lumines is addictive? Play Meteos for an hour or two. Then try to stop. Good luck.
And the girls are sure to love games like Nintendogs. Lovable puppies = instant love.
I could go on and on about the different games, there's really a lot of excellent titles out. And the DS is a bit less expensive.
Meanwhile, the PSP... well, it really doesn't have a killer app, there's no games that really stand out. It's great for playing movies... if that's what you want to do with it.