There's a couple early thresholds in progressing the Main Scenario that are important for crafting:

1) There's a level 15 quest that unlocks airship travel to the other two main cities. Since you started in Gridania, that quest will be "The Gridanian Envoy" (with equivalent quests for people who started in one of the other cities). This gives you access to reaching the other guilds and unlocking their classes. You've already seen that the Carpenter and Leatherworker guilds are in Gridania. The Weaver, Goldsmith, and Alchemist guilds are in Ul'dah. And the Culinarian, Blacksmith, and Armourer guilds are in Limsa Lominsa.

You can actually reach the Ul'dahn ones before that quest by going there overland. Central Shroud -> South Shroud -> Eastern Thanalan -> Central Thanalan -> Ul'dah. But most players just wait until they have access to flying there directly. And since Limsa Lominsa is on an island that you can't reach by foot, you'll have to wait for airship access to get to those guilds.

2) There's a level 17 Main Scenario Quest, "Scions of the Seventh Dawn", that unlocks the ability to hire retainers. Those are NPC assistants who do several things for you, including storing excess items so you don't need to hold everything in your inventory, and selling items on your behalf on the Market Board. Their extra storage space is particularly important for crafters, as you'll soon be juggling far more types of materials than you can hold. And if, in addition to making your own items, you're also planning on using crafting to make money, then you'll want access to selling what you make.