Hi, Elias, welcome to Elliquiy.
I second what IO said. I'm of the opinion that the books are about ten times better than the series, in all sincerity, so I would definitely recommend reading them, even if it's only for the kicks of getting to read a great story. That said, I'm afraid that there isn't much more to know about Melissandre, although she does get to be a POV character in the later books (I'm not there yet
), but you can learn a bit more about the Lord of Light and his workings through Thoros of Myr, a minor character, and the Brotherhood without Banners that Arya accompanies for a while.
And... there's a cult for Melissandre? o.O Curious, really. She does have a certain presence in the books, but to be honest, I'm a bit disappointed with her portrayal in the series. She _looks_ good, but to be honest, when someone says "Priestess," I tend to envision a lot more sensuality, or at least a certain enigmatic quality. When she recited a spell at the beginning of season 2, she said it as if she were going through a shopping list.