The tale of Genji can be considered to be the oldest story in Japan. Besides other books I currently read, ショッピングの女王 being one of them, The Tale of Genji ranges on top of my current to read list. Thanks to the fact that I keep listening to various Japanese radio stations on a daily basis, I already know the story up to the end of chapter 23, 初音 (はつね). I also greatly enjoy the story, having the laptop on my couch table, and just listening while relaxing on my sofa. One of the stations currently airing a version of The Tale of Genji, read by 「リンボウ先生」 which is the nickname of 林望さん (のぞみはやし) 「謹訳源氏物語」, is 調布FM.
As I already mentioned, this station is already very far into the story, so you might like to look for other radio stations just starting out with the story. Just do a google search for “リンボウ先生の「謹訳源氏物語」 ラジオ番組” and you will likely find one. If you like to read the story first, you might consider to buy the book after reading the review, or you go with the free version which you can find over at genji.co.jp if you prefer. I wish you a joyful time while you are discovering this ancient tales history, and the story itself, either by listening to the radio program, or by discovering and unfolding the story, by reading the book.