The progression after MSQ is up to you. You can set the goals that you want to. These are some common ones.

Challenges
  • Clear the latest extreme trial and farm it for the mount
  • Clear the latest 4 savage floors for the gear and mount.
  • Clear Palace of the Dead or Heaven-on-High solo.
  • Clear old content with Minimum IL and Silence Echo settings.

Grinds
  • Collect all relic weapons from all expansions.
  • Collect all mounts.
  • Collect all minions.
  • Collect all triple triad cards.
  • Get all achievements (not going to actually succeed at this, but you can spend years trying).

Social
  • Roleplaying.
  • Starting or joining a free company and chilling with them.
  • Hunting.
  • Starting map parties in party finder.

The extreme trials are unlocked from https://ffxiv.consolegameswiki.com/w..._as_a_Minstrel

The latest 4 raids are unlocked from https://eu.finalfantasyxiv.com/lodes...t/d5bc45b5af2/

The savage version of those raids are unlocked from Aporia where you got the normal ones from.

You can either join a static or pug them in party finder by joining a [Practice] party and then join a [Duty Completion] party when you have got 75-95% of the way through the fight.