Having read through the lists of Celtic Wicca, I feel very drawn to a number of the traditions, specifically the Deborean, Family, and Arthurian ones.
The Family Tradition appeals to me because it is the style of Wicca I was brought up practicing. My heritage is very much Irish (my mother's father was half-Irish), and a belief in the "little people" and the "fae folk" and the stories and traditions that encompass that culture were an important part of my childhood, thanks to my mother and grandfather. In my case, these beliefs and traditions were very much mixed with main-stream Christianity to the point that I didn't see a difference. Embracing the ability to see spirits, or speak with the dead, was one aspect. Leaving a cup of milk for the fairies was another. In my opinion, turning the Goddess Brigid into Saint Brigid (keeping her tale the same, bringing her out of hiding, yet still making her "acceptable" to share with others ) is yet another way. Even using specific herbs for a sore throat or making certain foods before a journey are more than family traditions because of the magical/mystical properties around the herbs and other ingredients. The people who practiced this form of Celtic Wicca kept their family's traditions and rituals by sharing with their children and their children's children.
The Arthurian Tradition also intrigues me. Based on everything I've been able to find, not only is this the most well-known of the Celtic paths, but it is also the one based upon King Arthur and the Knights of the Round Table. Each of the main characters in the legends is a hero of sorts. Deep at it's roots, this is a story of women's rights and empowerment. I don't believe that the legend is without truth, since by definition "Legends are fabulous stories that have some historical basis." (http://en.wikipedia.org/wiki/Legend#Related_concepts) I refuse to believe that there wasn't a tradition of Celtic beliefs to follow Arthur and his quest for the grail.
Finally, I think that's what makes the Deborean Tradition so appealing to me. It's a way of combining so many of the Celtic traditions with the Native American ones. The Clan of the Forest Moon relies on Cherokee beliefs (http://www.paganspath.com/forestmoon/principles-clan.htm), but I think any Native American tribe's traditions could be used. While this tradition seems to have been founded in the Smokey Mountains (http://josef.theislandbase.com/Wicca/AlternativeReligion.htm#deb), I don't see why the same principles can't apply to the people of the Black Hills. Since there is a strong Lakota population where I live, I think we as people should and could learn from the people who have inhabited this land for so long before us. I'm drawn to the "old ways" and in a country not even 250 years old, those ways really belong to the Native Americans.
No matter what "minor path" you resonate with, though, I think the Celtic traditions are the most "real" for me. I found the following definition at http://josef.theislandbase.com/Wicca/AlternativeReligion.htm#cel that summarized Celtic Wicca.
This sect concentrates on the elements, nature and the Ancients. With their great knowledge of healing, magick and nature, including plants, animals and stones, this tradition is probably the closest in structure to the ancients. They are extremely dedicated to preserving the importance of traditional Celtic values such as honor, courage, truth, strength, wisdom, and eloquence. Aided by the fey, Celtic magick is full of fun, yet powerful.
To me, that's what this path is all about.