The A Realm Reborn part of the story (1-50) is a slog and is getting adjusted during this patch cycle actually, but aside from MSQ for easy experience you can do some leveling roulettes and general dungeon runs for some more active leveling if you aren't feeling like doing quests all the time. But you will have to complete the MSQ stuffs to get into the expansion content for Heavensward and on. Of which you have 3 expansions worth of more story and reading dialogue and whatnot to go through still. Will be the case for most of your time until you reach level 80 and finish Shadowbringers.

I'm not an advocate for purchasing mog station stuff (if you ask me I say do your best to enjoy the MSQ 'cause it's really good post ARR), but there are story skip and level skip potions for sale if you want to get to endgame content faster. You will still have to do the MSQ for Shadowbringers and level from 70-80 if you do purchase the potions.

In Patch 5.1 next month we will be getting New Game+ to replay MSQ stuff from 3.X and 4.X. Since they're adjusting 2.X MSQ we'll be getting that probably in 5.2 or later for NG+.