It is in many ways a good idea to level all the crafting and gathering classes in parallell so they remain at roughly the same level.
There are basically two reasons for this:
a) That means they can share gear, which will greatly reduce the space needed for all their gear.
b) It means that when you are doing crafting you can gather and/or craft nearly all the materials needed by yourself instead of having to buy stuff from the Market Board.

Leveling your crafters along with your battle class(es) also lets you make your own gear, and thus be less dependent on lucky drops or buying things. It will also let you repair your own gear, and let you meld materia. (You probably haven't encountered materia yet, but you will.)


If I were you I would wait a bit with leveling crafter and gatherer classes until you have joined one of the Grand Companies. This will happen in a level 20 quest - you won't be able to miss it.
Reason for this is that doing the daily supply missions for your GC will give you lots of XP for your crafter/gather classes and is also an efficient way of earning GC seals at the start.



Waiting until you hit max level before you start leveling any crafters is of course possible, but that way you will have very little use for the items crafted while leveling your crafters.