Get The Bloomsday Book
Definitely read Ulysses, but you have to read one of the good guidebooks along with it or you'll miss everything. The book is both one giant literary pun as well as a complete encyclopedia on the entire history of Ireland, the Irish language and the Catholic Church. Also, he plays tricks on the reader and on his characters and even on the work itself--every chapter and most paragraphs have their own tricks, there are multiple layers of tricks. It took scholars 30-40 years to figure all this out and they're still not finished. Read the Bloomsday book or similar guidebook to get the highlights and the overall concept of each chapter. It's worth finishing because the ending is magnificent, and moving, and mind-blowing writing, but it won't mean as much if you haven't read what came before. Skim the Nightown episode, it can't be comprehended by anyone except Harold Bloom or Richard Ellman. As for Finnegan's, read the first couple of pages then forget the rest--it's not worth it and it doesn't have any "meaning," it's just like a long abstract poem. Enjoy Ulysses, it's worth it, it's richer than any other work you'll ever read, except Shakespeare and Dante. Certainly the richest modern work, you can't even imagine how rich a work can be until you get into it, it's very absorbing!!