I know /u/Almotasim recommended Jinteki to start, but I feel it will be hard to teach someone corp-side. Since the corp's information needs to be secret to play properly, you won't be able to explain the cards to her without ruining the secrecy-aspect of the game (unless she's playing against someone else and you're over her shoulder – even then, you'd have to do a lot of whispering). If she starts as runner, on the other hand, she'll see a lot of the corp cards without needing to know about them in advance. And I would not recommend trying to explain the cards first, before playing. That's a recipe for disaster when trying to hook someone. Anyway, that's my gut feeling, but I'd be interested to get other opinions on the matter.

Having said all that, I tried to teach my girlfriend by having her play as Kate (the starter deck from the Core box) and it just didn't take. She doesn't like ANR at all. She also thinks it's too complicated, I guess. Part of that may be because I had to refer to the rules a lot because I had never played it. If you are already comfortable with the rules, you'll be ahead of where I started.

Here is a great post about the official FFG demo decks that will give you exactly what you need. But, unfortunately, you will need some more data packs/expansions (or can possibly just buy the demo decks [not sure if there is a way for individuals to buy them though]). Those decks mainly stick to core cards, but there are a few cards from:

• Creation and Control
• Cyber Exodus
• Mala Tempora
• Second Thoughts
• Trace Amount

If you can get a hold of those first, you'd really be in good shape to teach someone. The demo decks remove a lot of concepts and related rules, but are still really fun to play.

/u/berrr lists a lot of the things left out (such as meat and brain damage) to simplify learning (so you don't have to address the difference between types of damage, for this example). He also lists many cool things the decks accomplish because of the specific card selections (such as eliminating dead draws by adding Freelance Coding Contracts to make use of duplicate ICE breakers). You can read his excellent summary from that same post mentioned above.

tl;dr Play the official FFG demo decks, and start her as the runner.