Here’s a guide on how to do things in order if you care about approaching it canonically. Big thanks to u/varorson for posting it on reddit and also u/ViddlyDiddly. The wiki also has its own story summaries which you may find here. Keep in mind that the story/dungeons/open world areas scale your stats down to the appropriate level, so you can always complete this content whenever you want and it’ll have some semblance of challenge. It’ll still be fairly easy either way, though. Most story mode dungeons can be solo’d, but it’ll be very challenging. 3 people minimum should be comfortable. Not everything has to be done. This is more for completionists/those who have an interest in the game's story.
Guild Wars 1 - takes place 250 years before the start of GW2. If you’ve played it, there will be interesting throwbacks and references but it’s not necessary to understand the story in GW2.
The Movement of the World - recaps what has happened in those 250 years between GW1 and GW2
Edge of Destiny - Book detailing the adventurers of Destiny’s Edge, who you’ll meet throughout the Personal Story and dungeons.
Personal Story - The original storyline that came out in 2012. It has its highs and lows depending on what decisions you make during character creation and throughout the personal story, but I do recommend doing it for the multitude of rewards it offers. Just remember that the story only gets better from here. The story mode of dungeons contain events that run parallel to the personal story, so you’ll want to sprinkle those in during the right story chapters. Here’s the order you can tackle it in:
Chapter 1 (unlocks at level 10)
Chapter 2 (unlocks at level 20)
Chapter 3 (unlocks at level 30)
Chapter 4 (unlocks at level 40)
Ascalon Catacombs Story (unlocks at level 30 and is content designed for 5 players)
Chapter 5 (unlocks at level 50)
Chapter 6 (unlocks at level 60)
Caudecus’s Manor story (Unlocks at level 40 and is content designed for 5 players)
Twilight Arbor story (Unlocks at level 50 and is content designed for 5 players)
Chapter 7 (unlocks at level 70)
Sorrow’s Embrace story (unlocks at level 60 and is content designed for 5 players)
Citadel of Flame story (Unlocks at level 70 and is content designed for 5 players)
Chapter 8 (unlocks at level 80) - up to the Further into Orr mission
Honor of the Waves (Unlocks at level 76 and is content designed for 5 players)
Crucible of Eternity (Unlocks at level 78 and is content designed for 5 players)
Finish the rest of Chapter 8, which includes the revamped Arah story dungeon which is now soloable
Living World Season 1 - ArenaNet’s first attempt at live content that evolved over time. It’s being added back in this year (2022) in addition to appearing in parts in some locations (Southsun Cove), fractals that revisit it, and activities). Some parts were amazing and some parts were just okay due to a release cadence that was a little too quick, but it’s critical that you understand the plot and characters that were introduced. DreamyAbaddon compiled a wonderfully made community movie with the events that occurred. Watch it here once you finish the personal story.
Living World Season 2 (complete pack = 1280 gems, was on sale for 896 gems previously) - Doesn’t require any expansions and is the lead-up to Heart of Thorns. You can play through this with a friend that owns it even if you don’t, but you will not receive any achievements or rewards. If you have a group of friends, one of you can grab it and the others can just join in. Focus on having everyone get seasons 3 and 4 first since everyone must own those to play together. Alternatively, watch it here.
Heart of Thorns expansion (Comes free with Path of Fire now) - Not much to say here to avoid spoilers.
Living World Season 3 (requires Heart of Thorns, currently 960 gems, was previously on sale for 672 gems. Supplemental reading: Notes from Rata Novus (Part 1, Part 2, Part 3). Alternatively, watch it here
Forsaken Thicket - 10 player raid (contains 3 raid wings), only requires Heart of Thorns and not Season 3
Conservation of Magic side story - not sure if it requires any expansions
Knight of the Thorn side story - Potential spoilers. Do this after finishing HoT
Episode 1 of Season 3
Transfer chaser side story - doesn’t require expansions
Justice of the Blade side story - doesn’t require expansions
Anomalous Occurrences side story - doesn’t require expansions
Episode 2-3 of Season 3
Bastion of the Penitent raid - 10 player raid, only requires Heart of Thorns, not S3
Episode 4-6 of Season 3
Path of Fire expansion - Read this before playing.
Hall of Chains - 10 player raid, requires Path of Fire
Living World Season 4 (requires Path of Fire, complete pack = 960 gems, was previously on sale for 672 gems
Episode 1
“Current Events” side story (doesn’t req expansions/Living World)
Mythwright Gambit Raid - 10 player raid, requires Path of Fire, but not Season 4
Episode 2-6 (after Episode 5, “All or Nothing”, read these)
The Key of Ahdashim - 10 player raid, only requires Path of Fire, not S4
The Icebrood Saga - new Living Story season rebranded to include “Expansion-level” content (requires Path of Fire, complete pack currently 960 gems. Previously on sale for 768 gems)
Prologue (200 gems if you missed out on it)
Episode 1 (Launched November 19, 2019.)
Episode 2 (Launched January 28, 2020)
Visions of the Past: Steel and Fire (Launched March 17, 2020) - Includes 4 missions from Season 1 to help bridge the gap in a weird out-of-order way. Stick to watching the movie instead of skipping to this point otherwise you'll hit a massive spoiler.
Episode 3 (Launched May 26, 2020)
Episode 4 (Launched July 28, 2020)
Champions Chapter 1: Truce (Launched November 17, 2020)
End of Dragons expansion
Secrets of the Obscure expansion
Janthir Wilds expansion
Visions of Eternity expansion (Coming soon!)
Bonus material:
Tyrian Travels (Ch 1, Ch 2, Ch 3, Ch 4, Ch 5, Ch 6)
Fractal storyline (Parallels main Season 3 plot):
I could write a book on the rest of the lore/story available, but I’ll leave that up to you to research/discover in and out of the game :)