After having gone through three phases of playing harvester and tradeskiller on top of the adventuring class, I've got a few recommendations for others looking to start up a tradeskill character on a non-legacy server.
1. I recommend waiting until you finish the airship pass Main quest before cracking the tradeskill container open. You do not need the tradeskill equipment to get to this point at all, but it will be quite helpful on the dungeon runs that are just around the corner from this point (if you can consistently HQ items). It is also highly likely that you will be doing quite a bit of shuttling around to get what you need, and the airship option will save you a LOT of pain. This advice is especially for these DoH classes in particular:
Armorer: Beginning Armorers need Ice shards, and currently the only low level accessible ice shards are in Central Shroud, all the way in Gridania. (Western La Noscea has Ice shards as well, but currently your harvesting class needs to be 16+ to harvest there.) Yeah, that's either an expensive teleport or a long run...or a 100 gil airship trip. This is tentative advice, however, pending Fishing being usable, as it is entirely possible they may let you fish out of Aleport at level 1.
Culinarian: You will need to level up Botany (and kill things), or things will slow down once you get to around 15. Again, long trip to Gridania, and quite a few of your goods that are not on the vendor are between the Shroud zones and Middle La Noscea. This is tentative advice, however, pending Fishing being usable.
Weaver: Lightning shards are in Central Thanalan. Cotton Bolls are in Central Shroud off of level 15 bushes. And given the quest text, I do not recommend expecting Cotton Bolls to stay on the guild vendor come Phase 4. Practically every recipe 14+ uses cotton bolls either directly or in a sub-component. No matter what you do, Bentbranch is going to be your home away from home and you are going to be shuttling frequently. (Or you will be spending a LOT of money for an obscene amount of cotton.) ...You will also want to get a dodo feather or two in La Noscea for your level 20 quest.
Leatherworker: You will need Aldgoat Skins. They drop frequently and in large quantities. The Goats you want are ~level 16+. (If you somehow find significantly lower level goats, they are only supposed to drop Animal Skin or Animal Hide.) When you finish the airship quest, you will be ~15 or 16, so you will be the right level to be plowing through them.
2. Pick at least one gathering class and take it to at least level 16. This will allow you to self-harvest all shards and at least Grade 1 Carbonized Matter for Materia. (Fire Shards are in East Thanalan or Middle La Noscea if you're not a miner, but you will have to level up to gain access.) Crystals are not available until at least level 30 nodes, if not higher, but once you find nodes with them, it is far easier to harvest crystals than to keep killing elementals over and over.
3. If you plan on doing multiple tradeskill classes, get ONE tradeskill class to ~11 first before starting on the rest. This is to unlock good/excellent/poor options and make the rest of the leveling even faster.
4. If you plan on leveling a gathering class to 20+, make absolutely sure you have a full stack (99) of carbonized matter for each gathering skill's level 20 quest. Botany has an easier time getting them (compared to Mining) because their nodes are right outside Aleport, so you don't have to turn on stealth to constantly avoid the anorexic wolves.
5. You only need 1 materia for your level 20 tradeskill quest item, even if it has more than one materia slot. (Although it's possible that may change in Phase 4.)
6. Join a Grand Company as quickly as possible, so that you can do the daily turn ins for seals and experience.
Too sleepy to think of any more right now.