The question of whether or not “first annual” is proper style makes me want to bring something up that isn't exactly on this topic, but is something that I found extremely valuable over the past several decades.
For anyone who has need of exact writing, or just a passing curiosity about proper usage, let me suggest a wonderful book, Roy H. Copperud's American Usage and Style: The Consensus.
I stumbled across this book (first edition), many years ago and found it to be more valuable than any of the several other style guides that I had been using in my work and studies. In this book Copperud looks at the leading authorities, style guides, and dictionaries, and comes up with a consensus on what is and is not correct. Over the years of using this book, I found it very striking that there was so much disagreement among the experts on what is or is not correct. I should also mention that there is a surprising difference in “correctness” between Canada and the US. After using this book for over thirty years I passed it on to my youngest son to hopefully help him with his work in graduate school.
I know that in this day of “Goggling” things, it isn't popular to use books, but this one was worth its weight in gold to me, (well, at least silver).
American Usage and Style: The Consensus: Roy H. Copperud: 9780442249069: Amazon.com: Books
Oh, and according to Copperud, “first annual” is correct. The objection to it is, in his words, “...just another journalistic superstition...”