I can understand your "lost" feeling after the first set of missions. It's tough making decisions with no goal in mind (end-game content, etc). But, take stock of what we do have.
As you've no doubt found, you are awarded 8 regional leves (faction/DoW-M/DoL) and 8 local leves (Crafting) roughly every 36 hours. Of course Faction leves only come up once you've earned x-amount of faction credits. The first set comes up after earning 100 credits. So, not to worry about those at the moment. Leveling up each of the War and Magic jobs is a pretty good idea, Rank 10 for them is a good goal and not that difficult to achieve. You can then swap around some of the abilities you learned to help beef up your favorite job. It's very open-ended so you can design how you want your character to be. Setting defensive spells/abilities can help you if you're more into solo play. If not, ask your LS mates how they would like you to fit into the group.
The local leves are extremely nice for crafting, they don't cost you any materials or crystals/shards. Be sure to read the card prior to accepting it so you know where to go to either make the delivery or pick up the materials. Be sure to puchase the starting tools from their guilds. There are several sites available with crafting recipes, even the Lodestone has some (though the ranks are generalized).
Balance your game play out. I wouldn't say to grind SP/XP all day on a War/Magic job nor craft all day. Do a little bit of both to keep from getting burned out, remember no real rush at the moment. Try not to teleport everywhere, save those points for the big trips. If you're in a group, only one person needs to spend the points for a teleport.
As for all those drops that your getting, I tend to vender what I can't use to craft with. It's pretty tough with the market wards the way they are to sell common drops. Your inventory will fill up fast as it is, with gear/weapons/tools eating into the space.
Just remember the game just came out, so at the moment there really isn't an end-goal so to speak. Unlike FF11 where we knew right away there were tons of missions and quests to be had at. For now I'd say try to make your own way, much like the adventurers of the past.^^
Pack your own lunch and bring nothing but Pixie Stix and Pop Rocks and get your liberty on.