If you're diligent enough you should have a party that can clear some of the last phase of this Soul Break fest event which should be in about 3 days and end in about 5. Even clearing Normal and/or Hard will give you a stash of XP eggs that'll be quite the boost.
But yeah, for now, keep clearing classic dungeons. The game basically has a set of progression content (the paintings) and time-limited events. Your first short-term goal should be getting a core team up to the point where you can obtain the Event characters from each time-limited Event. By the time the Tellah/Golbez event ends, you should be able to get them. They're a solid white mage/black mage pair.
What you need to know: The core class characters suck, and so does Tyro, but it's a tough choice when just starting the game on when to swap to other named characters you have since those named characters will start from lv1 again. Thankfully, the XP eggs mentioned above should help you boost some.
In terms of gear, keep in mind that the initial star ratings are very clear tiers of power, but also that Record Synergy (e.g. using FFIV gear in FFIV events/realms) is a huge boost.
In terms of abilities, to start off, Double Cut is a primary damage ability (2*) that is still key today. Elemental spells are a good bet for all-purpose damage, and you definitely want heals. Try to hone abilities rather than creating new ones - r3 is when they start to have enough lasting power for events and such.