Went heavy on the crafting here.
The base crafting crafts are Blacksmith, Armorer and Goldsmith. All the primary tools are created by these classes.
Secondary tool classes are Carpentry and Blacksmith, from what I remember. So for what we have so far (and I'm only listing for tradeskill and gathering related items)...
Armorer -- Relies primarily on Ice crystals and Mining for components. Creates Alembics (Alchemy) and Frying Pans (Culinary).
Blacksmith -- Relies primarily on Fire crystals and Mining for components. Also uses Carpentry sub-components (Lumber), Weaving sub-components (Cloth) and Goldsmith sub-components (anything Brass or stone related). Creates all Hammers (Armorer, Blacksmith, Goldsmith, Mining), Saws (Carpentry), Culinary Knives, Head Knives (Leatherworking), Files (Blacksmithing), Awls (Leatherworking), Mining Picks (Mining) and Hatchets (Botany).
Carpentry -- Relies primarily on Wind crystals and Botany for components. Also uses Blacksmith/Armorer sub-components (Ingots and metal parts). Creates Spinning Wheels (Weaving) and Grinding Wheels (Goldsmith). Also creates some tradeskill equipment (Shoes).
Alchemy -- Relies primarily on Water crystals and Botany and Mining for components. Creates some Wands (Conjurer) and books (Arcanist) and essential sub-components (like Rubber, Beeswax, Growth Formulae)
Goldsmith -- Relies primarily on Wind crystals and Mining for components. Creates Needles (Weaving) and CP increasing gear.
Leatherworking -- Relies primarily on Earth crystals, general monster slaughter and Mining for components (Alumen required for Aldgoat Skin and higher). Creates a significant portion of both DoH and DoL equipment (Head, Waist, Feet, Gloves).
Weaving -- Relies primarily on Lightning crystals and Botany for components. Creates the majority of DoH and DoL equipment (Chest, Head, Legs, Hands)
Culinary -- Relies primarily on Fire and Water crystals and Botany and Fishing for components. Some cooked foods give bonuses to tradeskills and gathering.
If your goal is to be as self-sufficient as possible in Tradeskilling, you should level everything other than Culinarian. That will cover all the required contingencies.
Carpenter is the easiest tradeskill to level due to the proximity of the available trees and wind crystals. You can easily level your Carpentry up with pretty much just lumber and wind crystals, but it'll be kind of boring. Blacksmith is in a similar boat, but you'd have to go to Western Thanalan instead. Armorer is not due to the need to go to Gridania with a Botanist for Ice crystals.
If harvestables and sub-components are removed from vendors, Weaving will be the most annoying to level. Moko Grass and Cotton Boils can't be harvested until your Botanist is level 11, minimum, and you will use A LOT of them. Leatherworking is a distant second since you need to claim mobs in order to get their drops, as far as I could tell, but you can still get a lot of skins when you're over-leveled.
Crystal farming with harvesting skills appear to be by zone. Out of the ones I've harvested:
North Shroud: Primarily Earth crystals
East Shroud: Primarily Wind crystals
Central Shroud: Primarily Wind crystals (with some Ice)
South Shroud: Primarily Wind crystals
Central Thanalan: Primarily Lightning crystals (with some Wind)
Western Thanalan: Primarily Water crystals (with some Fire)
Eastern Thanalan: Primarily Fire crystals
Middle La Noscea: Primarily Water crystals
I may have missed a few things in the mental info dump. But I'm pretty sure this information is correct.
Edit: Also, Carbonized Matter REQUIRES a level 16+ Gatherer.
Edited, Jun 23rd 2013 3:02pm by Ravashack