The item will only be given to one player, so there is nothing you can choose that will always guarantee you get it. For Pass, you're correct. That means you don't want the item. If everyone chooses Pass, then the item vanishes without going to anybody.

The distinction between Need and Greed is who gets the chance to roll for the item. You can only select Need if the item is designed for your current class. (For instance, as Archer, you can select Need if the item is designed for DoW classes that fill the DPS role. You cannot select Need for tank or DoM items.) Anyone who wants to can select Greed.

If anyone selects Need, then only those players who selected Need get a chance at the item. For example, if a DoW-DPS gear piece drops and the Archer and Pugilist both select Need, while the Gladiator and Conjurer select Greed, then the Archer and Pugilist would roll for which of the two of them gets the item. The Gladiator's and Conjurer's Greed choices wouldn't count, because Need always wins over Greed.

If *nobody* selects Need, then there's a roll between everyone who selected Greed, and the player with the highest roll gets the item. (This could come up either if none of the players are on the class(es) the item is designed for, or if the player whose class it is for already has the same item or something better.)