The main thought of course, as per everyone else who has also read it for the first time, is, finally finished reading it!
As some kind of comparison, since reading Ulysses, in a relative short space of time (a few days, although I have been on holiday...), I've read (albeit kid's books; read by my youngest; although a bit above her age) Killing the Dead by Marcus Sedgwick, Truckers by Terry Pratchett and Midnight Sun by Garry Kilworth.
It is difficult to know whether it really is genius or whether it is a manifestation of The Emperor's New Clothes. Interestingly, in reading the introduction/notes by Cedric Watts, which I purposefully didn't read until after the book, I found that opinion is actually quite divided about it. There are some, quite frankly, beautiful bits of prose, but there is also so much nonsense surrounding them that a) it is all too easy to tune out a bit and therefore miss the exceptional parts (also key plot points!) and b) hard to judge whether it's all a bit "infinite monkeys", did he really intersperse the drivel with genius or was it a fluke? Either way, you can certainly study, discuss and interpret this novel forever.
Reading Homer's Odyssey didn't help me. The paperback version of Ulysses I had didn't have the chapter names so whilst reading I found it almost impossible to see the parallels; I wasn't aware the connections were going to be so obscure though. I can see them afterwards, after reading the notes, but again I wonder if that is because these links really exist or whether people have just surmised them? The best example I have of this is that the chapter I was sure drew inspiration from the Sirens in The Odyssey, isn't actually the Sirens chapter; that other chapter starts beautifully, by the way: "The summer evening had begun to fold the world in its mysterious embrace".
The book starts off hard to read and seems to increase with difficultly with each chapter; apart from the chapter I thought was Sirens, but isn't, which actually seems to be written in normal English and is a breath of fresh air. You start off looking up words you don't know, but eventually give up because too many don't actually exist. Some entire chapters I don't know the significance of, even after reading the notes. By the last chapter you (well, me) are really hoping it relents a little and finally everything will come together, but it doesn't: this last chapter apparently has eight sentences; As far as actual full stops go though, I only counted two.
However, the news/press/print room bit is clever and the play/nighttime section at least reduces the page density and means all of a sudden you fly (well increase pace) through the book.
I feel for such an epic book I really should have more to say about it, but perhaps for now just acknowledging I've read it is enough since I probably need to read it again (and again) to even begin to understand it more completely. I'll give it at least a year before I do though; It is hard work.