I have a few friends that are going to be starting the game on Wutai very soon and they are concerned that they are already too far behind to catch up. So I've been giving advice on how to catch up more effectively and have constructed a To-Do list for them. I expect many people have advice that is better than mine so I decided to come to our server forum here and see what you have to say.
1.) Start off as DoW or DoM
2.) As soon as you can, go outside and grind to rank 5.
3.) Come back into town and complete the first quest line.
4.) Use the gil you got for as many crafting tools as you can get.
5.) Go pickup the rank 1 crafting leves for the tools that you purchased. (2 when you can 1 if that is all that is available.)
6.) Do these leves, you should be close to rank 5 for these crafts.
7.) Pickup all the Battlecraft leves that you can for the starter camp.
8.) Grind/Leve your DoW or DoM to rank 10.
9.) Complete your second quest line.
10.) Take new gil and buy the rest of the crafting tools.
11.) Do leves to get all crafts to 5.
12a.) Continue to grind/leve your DoW or DoM to rank 15.
12b.) Continue to grind/leve all crafting classes to 10.
13.) Complete third quest line installment.
At this point you have efficiently progressed while getting a strong feel for what the game currently has to offer. You will now have some idea of what craft you would like to continue to do, hopefully for profit. You will also have a grasp on the game mechanics which will help you pick a DoW/DoM class that fits your style and will have something to compare it against. By all means explore and enjoy the game, these are only suggestions to help keep you on track and quickly get familiar with the game.
There are many people here who are much further in the game and may have much better advice than I can give. I'm simply sharing what little I've learned in a month of play and what I would probably do if I were to have to start over again today.