First, I'll talk about Twilight. I don't personally like the books. They're entertaining enough, but they're very poorly written, to the extent that the majority of the characters are unrealistic. (Bella's father is a police officer and doesn't ever realize when she's snuck out of the house, for one example.) So go ahead and try them, but keep all that in mind.
As for other books. I assume you've read Harry Potter. If you haven't, you should read them.
If you're interested in more fantasy, The Golden Compass by Philip Pullman is great. It's mind-blowing.
Howl's Moving Castle by Diana Wynn Jones is one of my favorite books, ever. It's adorable. It's great.
Anne Rice is great, as far as vampire novels go. I've only read Interview with the Vampire, but it was amazing. I highly recommend it.
You may also like Robin McKinley's Beauty. It's a retelling of Beauty and the Beast from the perspective of Beauty, who isn't actually beautiful at all.
