You've probably gethered that any recommendations depend on what kind of game you are looking to run, including where things will be set. Rather than give you recommendations, here's my analysis of the books I've purchased in terms of my current game.
Player's Guide: this is a great book, well organised, with lots of useful info for players and DMs.
Five Nations: I've scarcely used this, despite my game--until recently--being set in Khorvaire. If you plan on moving the PCs about Khorvaire then it may be more useful, but much of the flavour is fairly bland in my estimation. I have a personal aversion to new feats, prestige classes being included for the sake of it in supplements, and I think this book is very guilty of that.
Explorer's Handbook: this is a kinda lame, but I have used the lightning rail and airship information. In fact, I've used this more than I imagined I would
Magic of Eberron: often these sorts of books make me come out into a rash--I end up with a slew of new feats, prestige classes, spells and magic items that I have to somehow disseminate to my players. Gah! Where this book is strong is emphasising the flavour of the types of magic addressed, so you get a much better feel of, for example, Zil elemental binding, daelkyr remnants, quori stuff, etc. Very useful if the magical elements of Eberron are likely to come into play (which in a standard Eberron game I think they would).
Secrets of Xen'Drik: I really like this one, and as my party are currently stranded somewhere in the jungle interior, I'm using it quite a bit. The material on Stormreach is blindingly dull in parts, but can be improved by porting in other material (I've used big chunks of Malhavoc Press's Ruins of Intrigue).
Of the stuff I've not bought, here's why:
Sharn: I've borrowed a friend's copy--it's great, but you already know that.
Faiths of Eberron: I use Green Ronin's Book of the Righteous for my Sovereign Host.
Races of Eberron: I don't use racial substitution/paragon levels for the PH races, so I see no reason to for the Eberron races either.
Dragonmarked: there's a guy on the WotC Eberron boards who has done a great write-up of the Dragonmarked Houses, so the official tome is a little redundant in my view. Plus, the free stuff has NO CRUNCH WHATSOEVER! Hooray!
Sarlona: I'm not really playing the psionics angle up much, plus there's no chance of my game heading that way soon. From a flick-through it looks excellent.
Hope this helped some.