You do it all on the same character. You will level everything, from magic, to melee, to crafting, to harvesting, all on one character.

As for skills, it's always good to level other classes for cross class skills. There's really no such thing as leveling a class unnecessarily. Sooner or later, you'll want it for something. Now whether or not you need to, I don't know. But it sure wouldn't hurt.