Welcome to FFXIV.
Here's some useful stuff to know:

1. The main story quests (marked with a flaming meteor icon) are mandatory for unlocking most content in the game so they should be your priority for progression.

2. Your class quest should be your second priority as they can give you new abilities and equipment.

3. At level 15 you can talk to a Smith npc to do Hall of the Novice exercises. The lessons are very basic for a MMO veteran but still worth doing as they give you some gear culminating with a exp boosting ring for level 30 and below for finishing the final lesson.

4. Quests that unlock content or game features are marked with a + sign and worth checking out. PVP is unlocked from one such quest at level 30 after joining a Grand Company in the story.

5. There are in game tool tips for what abilities do. The Balance Discord is a popular out of game resource for optimal endgame rotations.