Core book is most important, obviously. Covenants is the number-one suggested book for second purchase from people I've talked too, though Guardians of the Forest ranks up there too. For new players, I actually suggest a tribunal book (GotF!) so you have a framework to run the game in. It vastly reduces the amount of background, story, and plot work you need to do for the region and the local Order of Hermes; unless you're mostly ignoring the Order outside of chatting. My first Ars Magica game I ran was set without a Tribunal book so I wouldn't be bound into the pre-determined facts and I could make everything up without worrying about symmetry or consistancy... and then I found myself having to make up literally everything. It's a lot of work.
I really love the Covenants book, I think it's great for ideas, and it feels like a bit of a trap for new players due to the sheer number of complex systems it introduces. I think too much of Covenants relies upon finding ways to manage and micromanage your covenant resources.
I enjoy metaphysics, so I went pretty heavily into the Realm of Power books, but I don't see them as necessary unless your characters are delving deeply into any particular realm. The problem I run into with these books as 'new player suggestions' is the same thing I run into with the Houses books.... If you buy one, you really want to get the complete set, otherwise your faeries are not as well defined as your magical beasts... or your demons aren't distinquishable from your faeries in game mechanics... or you have a great in-depth study of the Flambeaux and the Verditius can't actually explore his deeper magical mysteries.