The dungeons start at level 15, so you may as well take some of the fedex quests for now. Also make sure to do all the quests that have the flame symbol around them. Those are the main story quests and you won't unlock anything unless you do them. In particular the airship which will take you to other cities is unlocked as part of the main story around level 15.

Its a toss up if you want the money or items for now. At level 6, I would probably take the equipment if you can use it. There is a quest soon to make sure all your gear is at least level 5. Once you unlock the first dungeon at level 15 you can start relying more on dungeon drops. Or just buy from the NPC vendors.

Once you get to level 10 you will be able to pick up other classes including the crafting. You will need to pick up Arcanist to eventually get white mage (you are still a conjurer). If you want to craft your own equipment you will need Weaver for most of it. Some of the recipes will also use things from Leatherworker, Goldsmith, and possibly Blacksmith but these can also be purchased from the market board.
Note that Arcanist and Weaver are not in Gridania, so you have to have unlocked the airship in order to get these classes anyway.

While you are leveling make sure to go back to the Conjurer guild every 5 levels and do the class quest there.
Until 15 your main leveling will be through quests, the hunting log, and FATEs or leves.