Having burned through storyline on my main (as I'd ignored it post 2.0) in bouts while farming for ilvl gear for primals through Crystal Tower; it really isn't that bad. I'm currently working on 2.1+ on my alt and its going a little slower because her gear sucks.
So:
1) unlock challenge log (in Limsa Drowning Wench level 15ish quest) Do dungeons/Fates/Leve at minimum each week
2) As archer, you'll have long ques so fate grinding while waiting is good. if you change to either healer or tank, dungeon burning can be good (arcanist is a good alternative if you want to dps and heal as you can be both past 30 and level both at same time, switching between Scholar to heal and Summoner to dps)
2.5) if you fate while in que, you'll quickly out level side quests. Leaving them for other classes later is an option. So long as you always stay ontop of your Main Story Quests
2.55) Doing Leve does help. At least unlocking each location is a good idea.
3) Do Roulette Every Day. if you que a dungeon specifically, que the one highest level on your list.
4) Post 30, unlock your chocobo companion (and start doing that challenge log as well) It starts in Camp Tranquil "My Fiesty Chocobo"
5) Fate grinding after 32/33 in Corethas is the fastest way to level. Either join a group, form your own; do a partial with chocobos out; it goes pretty quick.
6) around 46 you'll run into a dry spot in MSQ and side quests: fate farming here works better over dungeon farming unless your heals/tank (corethas still or northan than whichever has parties going)
6.5) doing Leves in Mor Dhona 45+ can also get you to 50 pretty quick if you set them at minimum 1 level higher then your level
At 50: Spend Soldiery as needed for accessories > gear; poetics for whatever you want/need most.
Finish up the first few MSQ until you get the credits and then pick up the next.
Start your Relic quest in Vesper Bay, do everything it says so you can get a decent weapon for starting 50. Upgrade to Zeinth asap (+1 of relic).
Also, pick up ALL the dungeon quests in Mor Dhona's tavern and the quest for Crystal tower (fresh 50 can usually run 1st wing labyrinth of the Ancients" right away)
gear up on that until you can run 2nd wing ST while still running the level 50 dungeons.
By the time you can run wing 2 you should be good for 2.1 and likely all of 2.2.
When you reach Wing 3 WOD you should be good for 2.3+ upgrading items as able.