If you plan on playing most, if not all crafting classes, I would suggest you start off as a blacksmith. Here are the reasons:
1. At level 10, blacksmith will learn Maker's Muse, which would increase your Standard synthe successful rate.
2. Blacksmith can make the level 7 main hand tool for most of the other crafting classes.
If you just want to do one crafting class, then you can just start the class you like and read on.
To start any crafting classes, you should start with their local leves in the city. Local leves gives you VERY good SP and exp for physical level, and they give you FREE mats to make the items (although you don't get to keep any extra items). Also, if you complete the quest, you will be rewarded with some mats most of the time, depends on which quest you did.
When you first start a crafting class, just get all available local leves for that specific class first. Some of the leves will give you the mats right away while the others require you to talk to a NPC to obtain the mats. If your leves contains rank 5 leves, don't do them just yet, pick the rank 1 leves first, but you can accept the quest first. Usually I would do the rank 1 leves in the city first, I can easily get to rank 3 from the first leve, and I would usually use the facility from the repair NPC for my first leve because I'm rank 1 doing rank 1 leve.
Then you can head out to the camp to do the rest of leves, and again, complete all rank 1 leves first. After 2~3 rank 1 leves, you'll be rank 5 if you succeeded 80% of the synthes. And now you can do your rank 5 leves with NPC buff. After you finished all leves for the first city, go to another city and the local leves for this class. Before you reach rank 10, you'll most likely need to go to all three cities everyday to get 8 leves.
On your second day, you'll see some rank 10 local leves on the list, but don't touch those until you hit rank 8 or higher.
If you also plan on playing a DoW/DoM class, it's wise to get the rank 1 leves at the same time you get your local leves. When you finish your local leves in the city, you can go to the first camp for the rest of your local leves, and after that, you can also do your rank 1 regional leves as well. By doing regional leves, you will be able to obtain some shards and mats for your crafting class. You can sell all mats except the one you can use with your crafting class.
After your first day of levequests, you'll be at least rank 6, now you can use the mats and shards you got from your leves reward or grind to level up your crafting class to about rank 8, so on the second day, you can do both rank 1, 5, and 10 leves. If you don't want to grind for mats or shards at all, then you can just wait until the leve reset and do the rank 1 and 5 local leves one more round until you hit 8, then you can start doing the rank 10 leves.