New to the game and need some help!

[Naberrie]

You do need to finish the level 10 class quest on your first class in order to unlock the Armory System, which allows you to save gear pre-sets for each class you unlock. So unless you want to change each piece of gear every time you change class, you need to do the level 10 quest.

And in order to gain a new slot in the Armory System you need to do the quest to unlock the class. Which is simply equipping the weapon and talking to an NPC. Also they give you the first weapon free so you don't have to buy anything.

Basically, just do the level 10 class quest, unlock the Armory System, then unlock the other classes at each guild the proper way. It's the easiest and best solution.

[Conradus]

You do need to finish the level 10 class quest on your first class in order to unlock the Armory System, which allows you to save gear pre-sets for each class you unlock. So unless you want to change each piece of gear every time you change class, you need to do the level 10 quest.
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No. The Armory System isn't just your gear sets. It's the whole system of being able change class by changing your primary weapon/tool. Until you do the level 10 class quest for your starting class, you cannot change class. At all. The other guilds will not give you the quest to activate their class.