Just wanted to add that, while there is no level requirement for joining an existing Free Company, you have to be at least level 25 to create one.
A few significant Main Scenario unlocks in the early part of the game:
The Ul'dahn Envoy (level 15), (or for those who started in other cities, the equivalent quests The Gridanian Envoy or The Lominsan Envoy), unlocks airship travel between the three starting cites as well as ferry travel between Western Thanalan and Limsa Lominsa. It also marks the transition between the city-specific portion of the main story and the combined portion, since after this, the stories merge and people do the following quests regardless of which city they started in.
The Scions of the Seventh Dawn (level 17), in addition to being pivotal to the story, where you meet some of the game's important NPCs, is also what unlocks access to hiring retainers. Retainers are NPCs who will do several things for you, including holding extra items and selling items on the marketboard.
In The Company You Keep (level 20), you'll join one of the three Grand Companies of Eorzea, either the Maelstrom of Limsa Lominsa, the Immortal Flames of Ul'dah, or the Twin Adder of Gridania. The first big gameplay advantage you get from this is that they'll issue you a mount through the sidequest My Little Chocobo, and getting your chocobo unlocks access to use of mounts in general.
And a listing of where you'll find the various class guilds (along with which jobs they become at level 30):
Uldah:
Pugilist (Monk)
Thamaturge (Black Mage)
Gladiator (Paladin)
Weaver
Goldsmith
Alchemist
Miner
Gridania:
Lancer (Dragoon)
Archer (Bard)
Conjurer (White Mage)
Leatherworker
Carpenter
Botanist
Limsa Lominsa:
Marauder (Warrior)
Arcanist (Summoner and/or Scholar)
Rogue (Ninja)
Blacksmith
Armourer
Culinarian
Fisherman
In adddition to these, the Heavensward and Stormblood expansions added additional jobs, but to unlock any of those you'll need to reach level 50 (and have the associated expansion).