Your bag is divided into 3 sections: Items, Crafting and Boutique. All quest items, gears, useless items goes to Items. In Crafting tab, all your profession related stuff goes there. Depending which profession you either have or will take - save materials for that/those. Each material tells in which profession it is used. Boutique tab is the most important as it contains your most valuable stuff - cash bought goods as well as vanity and some stuff you get in game like the daily Regular Customer quest reward for mount feed and incense.
As said on earlier replies, you can't sell quest items and they are marked with a small "?" on top left corner. Exception being Mark of Diligence for guild daily quests shown in Nandita's reply. You should save them all as you'll need plenty on them once in a guild.
As AO-Player said, all gray items can be sold and those are in the game to earn gold. I'm sure you know which are gears and weapons (greens, blues, purples) so before you sell, make sure they aren't better than you wear - all others you can just sell. Gear upgrading is end-game stuff.