Do the MSQ since that will lead you to most of the content and also give you a ton of EXP, lessening the need to run dungeons and Palace of the Dead for that first job at least. Also, do any quests that have a blue filling in the middle and a + sign on them- they unlock content like dungeons, aether currents for flying, and more.

I'd say focus on one job until you hit level cap, and after that, try anything you want. You can go back to your healer, try a new job, go into crafting/gathering, focus on your one job and gear it up to try end-game content- if it seems fun there's no harm in trying it. And by the way, welcome back!