Pandemic is absolutely brilliant - a modern classic for a good reason. And it's a great co-op game, so your GF may really like it because of that. My wife and I don't do loads of competitive stuff, so we've played a lot of co-ops in our time. Can't play base Pandemic any more though: she plays about ten games a day of the ipad version and so doesn't like the way I play the board version: too slow and don't make the right decisions.
If you find you like it, have a look at Pandemic Legacy, which is Pandemic with a story campaign. Stick with the base one for a while though.