This site lists all the MSQ quests.
https://ffxiv.consolegameswiki.com/w...ah_Quest_Chain
The LV 15 quest "The Uldahn Envoy" is the quest that takes you to other cities and unlocks airship travels. The two cities you go to are Gridania and Limsa Lominsa. When you arrive in each city be sure to attune yourself to the main aetheryte (preferably all in the city) so you can teleport there just like you do Ul'dah.

Once you're in Limsa you can start the quest to accept the Rogue job and work on that class.

There are no level requirements to join a Free Company (thats what guilds are called in this game), you only need someone to invite you to theirs. You can use shout chat in a city, novice network, or post on here that you're looking for a friendly FC and you'll get some invites.

After the "Hero in the making" quest at lv 20 you'll be able to choose your Grand Company. GC's are mostly background/story fluff as they're nearly identical. The main difference between them is each has some unique looking gear, there's no game mechanic thats influenced by your GC.