Changing Classes

[Estellios]

But like, when I went to Brother E-Sumi or whatever, I couldn't pick his quest up as an Arcanist, and that was the only quest available. Did I perhaps forget where I left off and I need to go find that other quest?

You must have just forgot to get the next leg of the main story quest, if you are in Limsa and are able to travel by airship you are probably on the quest to unlock the first dungeon. Check this list and find out what the last quest you did is (you can check in your journal) and what your next quest is and who starts it.

Just FYI, main storyline quests are the ones with the fiery looking quest symbol.

E-sumi is for your class quests as was mentioned.