As mentionned in the previous answers, getting all crafts at lvl 15 (for cross skills) is a great start.
Alchemist 15 : Tricks of Trades (ToT)
Culinarian 15 : Hasty Touch
Carpenter 50 : Byregot's blessing.
Those 3 skills will be your best friends forever.
There are a few things which are worth reminding. CP are your most useful stat. The more CP you have, the more moves you can make and the more options become available to you. Keep your gear up-to-date.
Some words about gathering :
Miner will help you greatly if you dedicate to Goldsmith / Armorer / Blacksmith
Botanist will help greatly if you dedicate to Culinarian / Carpenter / Weaver
Alchemist's and leatherworker's raw materials can be gathered from mobs (wings, fangs, skins..)
Fisher, well...The fishes can be used in a few culinarian recipes (less than 15, out of many hundreds of recipes) and a few alchemist recipes. It's definitely not the mot urgent gatherer to have.
In my opinion, the easiest crafters are the ones which use botanist's items, as they are easily obtainable even in HQ. And as you need Hasty Touch and Byregot's blessing, I think it should be your first choice.
When you level up carpenter and culinarian (especially CUL), you don't need every mat in HQ. You should have some fun and try with full-HQ mats, and when you realize it's easy, remove one and use an NQ instead, and when that gets still too easy, remove another. That will improve your "intuition" and knowledge of skills, and will perfect your rotation along the way to 50.
About the auto-synth and the outside help from friends, why not, but I'm not too sure this is a reasonable idea. The whole point in levelling is to learn. You don't want to reach 50 or even 60, and realize that you do not know your skills at all. Nobody wants a fighter who levelled up exclusively through fates, as it's likely he can't master his skills. It's the same for crafters, IMO.