While there are allusions to Golden Dawn materials in the deck, Waite had his own mystical meanings in mind. You'll get further reading his own book on Kabbalah if you really want to understand the symbols and not just learn the Golden Dawn system. Likewise his books on Freemasonry are essential, as are his summaries of the writings of Eliphas Lévi, and more.
Yes, he saw himself as a mystical Christian (but not an orthodox one) and books like The Cloud of Upon the Sanctuary and Evelyn Underhill's Mysticism help in understanding what this meant to him. It becomes clear in reading Waite that mystical Christianity is merely an extension of a "Secret Tradition" that has always been with us. It is found in ancient myths and the practices of Eleusis, the Egyptians and those of the Middle East, and in the Grail myths and Freemasonry. The High Priestess, for instance, is the Shekinah, Sophia, Isis and many more. So, it is perfectly appropriate to read the cards, especially the Major Arcana, with Pagan allusions, or Kabbalistic ones, or mystical Christian ones. For Waite, they all reflect a deeper Truth that lies behind all of these. If you miss this, you miss what he was really trying to convey.