FFIX is a good game. It has a great storyline and nicely developed characters, and it's set on an interesting world with lots of traditional FF elements. Some of its cameos might be hard to understand, but it still lets you appreciate the old-school FFs better than by playing some new FFs, like FF7, FF8 or FFX. Even though FFIV is an excellent game and it's also a lot like FFIX, I thought it was the hardest FF game, especially with the Hard Type. That's why someone new to RPGs could easily get frustrated with the game.
The Captain, just remember to encourage your friend to play FFIX and tell her to have fun with it, and after that, try to get her to play some other RPGs too. :) It would also be good if she learns to like RPGs for their gameplay and story, not for their eye candy.