In this case, "are of" is only being used because of the following word, "importance". It's a far more proper way of saying, "are important".
And to rewrite this sentence, a more natural way you could say this is: "choose books that you feel are important to you." or simply "choose books that you think are important".
Don't forget the "are" in sentences like these! "Are" is being used in place of "is" because "books" is plural. If it were a single book, "is" would be used, instead.