Regretfully, I was unable to hike this when I was there a week ago. The trail remains closed through the end of October,as they are trying to repair the trail, clean up some of the litter and from what I understand, evict some of the squatters at the far end of the trail.
From talking with people (and certainly there are many on this site who've hiked the whole thing), the trail is quite scenic and fairly challenging because of the hazards associated with hiking along cliff sections.
The rainiest months are November through January, and that part of the coast, being very lush, receives a lot of showers and the peaks are often cloud-covered. It was so warm while we were there I don't know how much use a jacket would be, as the temperatures are generally warm enough to cause one to perspire in his or her own jacket.
I hiked in the Waimea Canyon area and enjoyed it, even if it wasn't a solitary experience (there are plenty of people hiking in that area - it's popular). Bring plenty of water, especially if you are not used to tropical climes. Access is on the other side of the island, around a two-hour drive from the north shore under normal traffic.
There is a book on Kauai Trails, called, appropriately, "Kauai Trails" by Kathy Morey. Issued by Wilderness Press (ISBN 978-0-89997-305-0), I found the book quite informative, however, the maps inside are extremely basic and are no substitute for a good topo map. The book does have a good description of the Napali Coast, plus a number of other trails ranging from a stroll to a tough hike. I would recommend this book because it will give you plenty of ideas.
Finally, I hike with poles and did bring them to Kauai with me. I found them to be useful in the wetter areas....
Have fun and enjoy