With every story I've ever encountered- whether it was a book, a movie, a TV show, anything- I've always loved character first. They have to have great characters. Without them, I might appreciate a story, and even respect it, but I will never love that story if I don't truly adore at least one of them. Even if it's one that I love to hate, or wish I didn't love.
The problem with getting into the Song of Ice and Fire books, and watching A Game of Thrones, is that I can't help but love a lot of these characters, and there are a lot of them to love. But with this story, I know it will only end in tears.