Some Questions

[Nutz]

Best way to level crafters is with leves (and Ixali quests -- though they're a bit limited). I'd go ahead and progress WVR ahead of the others, but still do the Ixali quests daily. Reason being that the final tier of daily quests can be a bit tough at the appropriate level (though super easy at 50+) and you can just complete those quests on any class (WVR) and turn them in on whichever class you actually want to level (that's how I leveled ALC almost entirely and a lot of CUL).

Also be sure to turn in items to your grand company daily, especially if the item has a star next to it (double exp). Always turn in HQ (again double exp) only for leves and GC (unless you somehow can't). Some leves are better than others, but generally the ones that require travel will bring in the most gil for the effort (unless running feels like a lot of effort).

For gathering, leves aren't so great. They work, but are much better spent on crafters. Turning in HQ items to your GC daily is very nice for gathering professions though. It requires nothing but time, as opposed to perhaps better gear and luck with a crafter. Moreover, the side effect of gathering those HQ items is that you gathered a bunch of stuff to craft with or sell.

Turning in a bunch of stuff to your GC will allow you lots of seals for purchasing engineering and survival manuals which are always handy (+50% exp capped at 40k or 2 hours, whichever occurs first). Other than that, WVR, LTW, and GSM are the classes that will most help you progress with crafting and gathering in general because they produce almost all of the equipment (BSM makes most tools). Eventually you will probably want all classes leveled, and if you stick with doing the Ixali quests that will be fairly easy to achieve eventually.

Also, don't be shy about buying turn in items if you have more gil than time. Sometimes they're not even expensive.

EDIT: wasn't sure what you were saying about the Ixali quests, but yeah, if you made a NQ item just throw it away and talk to the NPC again. They were apparently given a bottomless bag of ingredients to provide you with. You only provide the very small number of shards. If you're having trouble you can look up some 2.x crafting guides, though most are suited for omni-crafters with access to every ability. Might just take multiple tries with whatever you've got.