Inspired by 
rachelmanija, I got Edward Seidensticker's translation of The Tale of Genji out of the library last night and read the first two chapters last night.
This may be Exhibit A in the case for my shallowness, but my verdict so far is "unintentionally hilarious."
Chapter 1, "The Paulownia Court": In which Genji is born and is wonderful.
rachelmanija has a more detailed and useful summary of this chapter. The main thing I got out of it was that everyone thinks Genji is too good for this world; I actually found myself thinking "show not tell!" about his purported wonderfulness, and normally I dislike that phrase [*]. Also, people are apparently fungible, at least if they look enough like one's dead lover; and there's nothing wrong with having a terrible crush on the woman who's taken one's mother's place.
[*] I've seen too many people tie themselves in knots to avoid telling, or coming up with ever-finer distinctions between telling and showing, when, in fact, one must use words to convey one's art, and so reduced to the most literal level, it's all telling—unless one is creating sequential art. Far more useful to think about the appropriateness of exposition for the situation one is in. End rant.
As people said in comments to rachelmanija's post, whee, shoujo tropes! (I've not read any specifically shoujo manga, though Saiyuki has some shoujo influences; but hanging around discussions of manga and anime has given me some familiarity.)
Chapter 2, "The Broom Tree": In which men talk about women they've screwed over and Genji gets obsessed with yet another woman.
What I got out of it: all failures of romantic or sexual relationships are the fault of the woman for failing to balance, to the man's taste, (a) assertiveness against rotten treatment by the man and (b) forgiveness for rotten treatment by the man. At least, according to the windy conversations of the men in the first part of the chapter.
I laughed out loud when, during these windy conversations, we are told that
Genji . . . was wearing several soft white singlets with an informal court robe thrown loosely over them. As he sat in the lamplight leaning against an armrest, his companions almost wished he was a woman.
I also snickered at the end of the chapter, but quietly since Chad had fallen asleep: Genji has dragged a different woman than his mother-substitute off to have dubiously-consensual sex, without even seeing her first, and then ardently pursues her through the messenger of her 12 or 13 year old brother. She rebuffs him on considerations of honor, so he says:
"Well, you at least must not abandon me." Genji pulled the boy down beside him.
The boy was delighted, such were Genji's youthful charms. Genji, for his part, or so one is informed, found the boy more attractive than his chilly sister.
It's the sudden jump from subtext to text, plus the random "well, since you're here, even though I've shown no interest in you or your gender before now," that made me snicker.
(rachelmanija's summary of this chapter is here.)
Okay, more seriously: characters obviously aren't going to be the thing that pulls me through this. The introduction has warned me not to expect narrative momentum or structure, either. I'll read a few more chapters at least, for the unintentional hilarity, the historical and cultural content, and some of the language; but it's a long damn book and I don't know how far I'll get. On the other hand, I haven't been reading a lot lately before bed, and this is very unlikely to keep me up reading. We'll see.
Edit: an online edition of the Seidensticker translation: chapter 1, chapter 2 (oddly their introduction is not Seidensticker's). I'm also collecting other people's comments in my memories.