Though I've recommended that you read through Dubliners completely and sequentially, be sure not to miss reading "Araby" and "The Dead".
A key concept we will be discussing is the Joycean "epiphany." Here is the definition of epiphany as Joyce wrote it into this excerpt from Stephen Hero: Joyce's definition.
I've also had the good fortune to study with Prof. A. Nicholas Fargnoli, President of The James Joyce Society, and one of the finest of Joyce scholars. Here are links to two of his most resourceful books on Joyce:
You might also be interesting in exploring the James Joyce Centre in Dublin, and the World Wide Dubliners site, which includes an introductory essay by Wallace Gray.
For you film buffs: John Huston's film version of The Dead
was released in 1987, featuring his daughter, Anjelica. The DVD version
is out of print and is Region 2 encoded. But used copies are still
available in VHS: The Dead.