Based on the words of Urien, Ovarwa, and everyone else, I'm revising the answer. This will eventually become the new FAQ entry. I think I will edit this post to keep it up-to-date as new remarks get folded in.
[Edited in response to YR7's comments]
Q: Which books should I buy?
A: The quick answer is, all of 'em. They're all good.
A more thoughtful answer depends on whether you're a player or storyguide, and on what your saga is like. High adventure, or low intrigue? Lots of politics, or not so much? Young magi just getting started, or Archmagi in the twilight years of their power?
The only book you strictly need is the ArM5 rule book. All the other books are supplements that extend the rules and/or setting in certain ways.
If you are a player:
The House book for whichever House your magus belongs to is probably most important. They give a lot of information that puts each House in context.
If you are a storyguide:
You should seriously consider acquiring whatever books your players have for their own characters' Houses. It's better than constantly borrowing the books to plumb them for ideas. Apart from that, here is a bit more on what each book has to offer.
Covenants is a toolbox for creating your own covenant(s) with lots of new Boons and Hooks, vis sources, and ready-made NPC's; rules for covenant income, finance, and morale; also extended book rules, laboratory customization, and rules for using Rego spells to create crafted items.
Guardians of the Forest: Includes Durenmar and the Great Library, plus the idea of Forest Paths and Forest Spirits, which may be useful in a saga outside the Rhine.
Houses of Hermes: Mystery Cults: Rules for designing statistics for mundane beasts; plus, obviously, details on the Inner Mysteries of the four Mystery Houses, which some players consider essential.
Houses of Hermes: Societates: Rules for designing your own non-Hermetic powers for House Ex Miscellanea, plus several examples; expanded rules for illusions and for crafting mundane items with magic; rules for fighting invisibly and for spells of attack that bypass Magic Resistance; rules system for debate and social skills.
Houses of Hermes: True Lineages: Lots of information on Hermetic Law; rules for original research; rules on the use of Intrigue (plu Guile and Folk Ken) -- though note that these are not precisely concordant with later rules published in HoH: Societates
The Mysteries: Revised Edition: Mysteries can provide a worthy goal for senior magi; mystery societies also make useful adversaries. There are some new Virtues and Flaws and laboratory options that are accessible to non-Mystery magi. It also includes rules for memorization and the new Academic Ability, Art of Memory.
Realms of Power: Infernal is a good choice if you are looking for enemies (either straightforward or subtle) for your PC's to fight.
Realms of Power: Divine adds possibilities for pious magi and companions, including supernatural powers; it also outlines the major religions of Mythic Europe
More to come...