While it is invaluable for working with the Thoth to have a basic knowledge of astrology, the kind of astrology that is most relevant to Tarot is the astrology of the decans. This is a topic that modern books on astrology usually don't even touch. For studying it, I recommend most of all Austin Coppock's book 36 Faces.
If you are interested in how I started learning the Thoth, here goes. Among a number of popular decks, it was simply the one which appealed to me the most. I bought the deck and soon started reading with it, having as my guides the two only books that were available in German at the time, the BoT and Ziegler's Mirror of the Soul. It was learning by doing, really, but it expanded to an ongoing study of astrology and of the Kabbalah.
The Thoth is like a manual of metaphysics, it incorporates the teachings of many Western and Eastern systems, reflecting AC's great knowledge. If you need to familiarize yourself with all of that before even touching the deck, chances are, you never will! I suggest, do this in reverse: Start with the deck and work from there.