That's a tall order... there are so many little quests that are helpful, but not necessarily essential.
The essential questions are still probably
Rank 2 at Level 10
Subjob at level 18-20
Chocobo at level 20
Rank 3 at level 25-30
Advanced jobs at level 30
Abyssea Starter Quests (talk to Joachim in Port Jeuno) at 30**
Rank 4 at level 40
AF weapon at level 42
Rank 5 at level 50
The genkais, all 10 of them, from level 50-95
Your AF armor at level 52-60
Rank 6 at level 60
75+ - Abyssea quests, all expansion missions, remaining ranks
**Joachim is probably the single most critical change in this essential order. Talk to him as soon as you hit level 30, so you can start collecting traverser stones. That way, by the time you're ready to level in Abyssea at 75+, you have enough stones built up to not get kicked out after 30 minutes.
____________________________FFXI: Catwho on Bismarck. Once again a top bard on the server: Dardaubla 90 on 1/6/2014
FFXIV: Katarh Mest on Lamia - Member of The Swarm and leader of Grammarian Tea House chat LS
I can't understand anyone who skips the cutscenes of a Final Fantasy game. That's like going to Texas and not getting barbecue.