I was wondering this too if there is a tarot corresondences 101 book, so I can know whats what and which would be worthwhile for me to investigate. That's the question you hit on here which ones would be good for me to know. I have no idea.
Susie's book will be out next year. Until then ...
The thing about the correspondences is, that you have to have some interest in not only the actual correspondence but what is corresponded too. So, for instance, if you have some interest, and knowledge of Astrology (or are prepared to learn the basics) you could start with the standard Golden Dawn (GD) correspondences and then see how they work for your readings and Tarot work. Why do I mention the GD? Well IMO it's a good place to start. If one accepts that 'most' decks are based on the RWS then it kinda makes sense to use the GD. The other systems (Piobb, Balti, etc.) are often associated with specific decks, or styles of decks.
Getting into the Hebrew letters and the Kabbalah can be fascinating, and illuminating. If you have zero interest in Kabbalah though it would be a waste of time and energy. I myself have absolutely no interest in what card correspond to what Herb, but there are many that do and then utilise that knowledge for spell work and (I'm guessing) woohoo cooking.
Now there are some who argue (often convincingly) that correspondences are a load of horse-doodoo. I heard a chap recently incinerated a RWS deck live on Facebook to make a point that his return to TdM decks was a liberation, and burning the RWS and all its links to the GD and its myriad correspondences was akin to burning a bra in the 60s. Let's not get into the OTT nature of that event, or the fact it was a chap invoking a feminist image.
So what decks do you use or have a preference for? That could well determine at least a starting point. If indeed your initial interest should commence with the GD, here is a nice, clear, straightforward set of the basic correspondences (Astro is at the bottom of the page):
http://www.billheidrick.com/works/tarottbl.htm
Ravenest has a lovely turn of phrase, and I think he's spot on; for me, being terribly myopic, it's like looking at a card with my glasses-less fuzzy-focus eyes, as opposed to seeing it all in sharp clear focus.
Re Barleywine: I've still not got my head around the I Ching links. To my knowledge the sadly departed Mithros is the only deck designer who attempted it with his deck The Mutational Tarot. I'm a babe in the woods with it but his justifications and logic are hard to fault. Mind you there are some leaps of faith to take with it. Either way it's a provocative deck and a fine effort.
Stephen Skinner's book, "The Complete Magician's Tables" (Llewellyn, USA, 2008, ISBN 9780738711645) is a weighty attempt to collect all manner of correspondences and 'stuff'. It might be overkill for your purposes, but I highly recommend it. There are others but I think Stephen's book is the most comprehensive, and he's very upfront about his own prejudices and reasonings.