I found the book to seem mostly non-essential. On the PC side of it, I would probably go magic of eberron, races of eberron, player's guide (assuming I play a lot more non-Eberron games), then core Eberron book 4th (assuming DM has this one already). If I am doing mostly or only Eberron, then I'd go player's guide, magic, races, core.
As a DM then it would depend on what kind of game you were doing, but in this case core is obviously the most important for actually running an Eberron game, then either Explorers or Five Nations (ie if you are mostly adventuring in Xendrik, then explorers is clearly more useful than 5 Nations. Sharn is just too specific unless you are spending most of your campaign there. If the PCs are usually only there during downtime or even just an occational adventure, I wouldn't bother picking it up until I had both Explorers and 5 Nations. Races might also be worthwhile for the DM if he also does non-Eberron games and might want to include these Races in the world he makes up.
