Lacedaemonian said:
George RR Martin's A Song of Ice and Fire series is a must read.
I agree, it certainly is ... but not for somebody brand new to delving into sci-fi, and not for somebody who specified
sci-fi. Not only does it conflict with the shows she indicated she enjoys, but you'd be pushing her into a big, dense, and most importantly
unfinished fantasy work. Too much too soon, in my opinion, and as likely to turn her off as it is to draw her in. Some 4,000 pages of a story that isn’t even finished is some welcome. I utterly adore Martin's brilliant series, but it's not something I would hand to somebody new to this world.
Annabel, if you're somebody who grew to love sci-fi via the screen and who is just now starting to explore the rich and rewarding world of science fiction and fantasy literature, you might want to consider reading some of the franchise book series out there tied to the franchises you love. Star Wars, X-Files, whatever. There are tons of them, and while longtime genre readers are prone to scoff at such works - admittedly, I'm one of those that do - they will offer you very comfortable first steps in sci-fi reading, all in worlds you enjoy with characters you already love.
Timothy Zhan's Star Wars books are a good start. Quality writing and great stories. His Thrawn Trilogy (the first book is Heir To The Empire) picks up where Return of the Jedi left off. Great books, new characters, all your old favorites, excellent action, superb villains. Pretty much all you could ever want out of new Star Wars stories. You’ll enjoy the reading experience. (To show you the esteem these are held in, many Star Wars fans call these Episodes 7, 8 and 9).
By then you will have no doubt decided that you love reading sci-fi. Explore other Star Wars books, or even better, branch out into all the world of SF has to offer.
If you want to go right for the best,
this list and
this list offer good starting points for literate, thoughtful, time-tested science fiction and fantasy. Just bring up the titles on Amazon, read the blurbs, and see what appeals to you. And then buy it! It will be hard to go wrong with most of what is on these lists. (I’ve read a good number of books from each list, with very few I did not care for). I would suggest you read about a few of the titles here that catch your eye and ask about them. Get opinions here and elsewhere. And then buy! And read!
The big three of sci-fi are Arthur C. Clarke, Isaac Asimov, and Robert Heinlein, with Clarke the most accessible of the three. Fantasy is a little more wide open. There are Tolkien and his imitators, the Not Very Tolkienish, and a whole world beyond. (But I get the sense that sci-fi is your preferred genre for now).
If on the otherhand you prefer lighter fare, perfect for a lazy Saturday afternoon and packed with action, the franchise books will suit your needs until you are ready to move on. I know folks who get each Star Wars book as it comes out, devouring them. There must be 100 of the damn things, with an ongoing story (I think) in the recent ones.
Anyway, enjoy.