Reddit reviews Pagan Portals - Irish Paganism: Reconstructing Irish Polytheism

There are different valid starting points, and I think which one would be best depends on your interests, desires, and knowledge level.

If you're a Hibernophile who is itching to delve into Irish history and culture, or if you wish to read some epic and fantastic tales, then jumping into the mythological cycles is a fine starting point. The pro to this would be that you would be familiarizing yourself with the biggest bulk of Gaelic polytheist source material right off the bat. The cons would be that this literature alone is probably not going to give you much of a conceptual framework for polytheism and how to practice it, and you will certainly want to purchase a hard-copy with a reputable translation (unless you are fluent enough in Irish already) and annotations in order to properly comprehend the material.

If polytheistic practice is your biggest draw, then I would recommend starting your journey outside of Irish literature by examining the actual Celtic pagan archaeological remains at our disposal. The con to this would be that the majority of the material you examine is probably not going to be Irish. The pro to this is that it represents actual pagan and polytheistic practices that can inform us how our ancestors approached the gods and how we can do so as well. For this, I would recommend the somewhat misleadingly named Celtic Mythology by Proinsias MacCana. It is a highly accessible and enjoyable introduction to Celtic archaeology and it does an admirable job of connecting the archeological material to the later written mythology. You may also want to explore www.polytheist.com and J.M. Greer's A World Full of Gods.

Unfortunately I am not very familiar with literature about Gaelic folk culture, but that is another potential starting point. The pro being that it's Gaelic and would be full of practices and worldviews you could immediately adopt. The con being that many of those practices and worldviews are not completely (or even partially) pagan. I know many CR's are quite fond of the Carmina Gadelica, though I don't know of any other recommendable books outside of that.

If you are a total neophyte and those aforementioned avenues seemed daunting, then I would recommend Peter Berresford Ellis' Celtic Myths and Legends for a more modern and digestible rendition of the Irish and Welsh legends, or Morgan Daimler's Irish Paganism for a general overview of beliefs, practices, and source materials for Gaelic polytheism.