Elder Scrolls Online has an insane amount of story rich content and, thanks to the One Tamriel update, it also has freedom. Unfortunately, with that freedom comes confusion. You can do anything in any order in this game, but as far as chronology is concerned, there is only one correct order. To make things easier for everyone, I have created this guide in order to streamline and simplify your Elder Scrolls Online experience. Let's begin with the alliance quest lines and the main quest line.

Quests from both the alliance zone quest line and the main quest line take place at the same time if you do them in the right order. Before the One Tamriel update, this was done automatically because quests were level locked. But now we must take matters into our own hands.

Once you complete the starting tutorial quest "The Gates of Adamant", you will find yourself in a portal room. Your options are as follows:

If you own the base game:
Stro's M'Kai
Kenarthi's Roost
Bleakrock Isle
Vvardenfell

If you own the applicable chapter or are an ESO Plus subscriber:
Summerset Isle
Elsweyr
Greymoor
Blackwood

It is recommended to begin in the prologue zone relevant to your alliance.

Below is the proper order for each alliance followed by the proper way to weave in the main quest line.

The Daggerfall Covenant:

Prologue: Stros M'Kai
Prologue: Betnikh
Zone 1. Glenumbra
Zone 2. Stormhaven
Zone 3. Rivenspire
Zone 4. Alik'r Desert
Zone 5. Bangkorai

Aldmeri Dominion:

Prologue: Khenarthi's Roost
Zone 1. Auridon
Zone 2. Grahtwood
Zone 3. Greenshade
Zone 4. Malabal Tor
Zone 5. Reaper's March

Ebonhart Pact:

Prologue: Bleackrock Isle
Prologue: Bal Foyen
Zone 1. Stonefalls
Zone 2. Deshaan
Zone 3. Shadowfen
Zone 4. Eastmarch
Zone 5. The Rift

Main Quest:

"Soul Shriven in Coldharbour" should be completed as soon as you arrive in the first zone for your alliance. You need to find The Benefactor to begin this quest.

He's located in the following places:
Vulkhel Guard (Auridon): The Interim Suitor
Daggerfall (Glenumbra): Patheirry House
Davon's Watch (Stonefalls): Sadreno House

"The Harborage" should be completed before you begin the alliance zone questline.
"Daughter of Giants" Zone 1.
"Chasing Shadows" Zone 1.
"Castle of the Worm" Zone 2.
"The Tharn Speaks" Zone 3.
"Halls of Torment" Zone 3.
"Valley of Blades" Zone 4.
"Shadow of Sancre Tor" Zone 5.
"Council of the Five Companions" should be completed immediately after "Shadow of Sacnre Tor".
Before you go any further you'll complete the neutral quests "Messages Across Tamriel" and "The Weight of Three Crowns". Each alliance has a different version of these two quests but they tie all three alliance quest lines together along with the main quest line.
After these quests, you'll complete a series of quests in Coldharbour.
Then, you will complete "The Final Assault" which is the final Alliance Quest.
Finally, you'll complete "God of Schemes", which will wrap up the Main Quest line.

After completing all of this, you can take it a couple steps further by completing "Cadwell's Silver" and "Cadwell's Gold" by meeting up with, you guessed it: Cadwell, who is located in the Harborage. These two quests allow you to gain access to the other two alliances' quest lines.

Here is a tremendously helpful graphic from The Unofficial Elder Scrolls Pages:

The Mages Guild and Fighters Guild quest lines both take place during the alliance and main quest lines. Simply complete one quest for each guild per zone. To begin the quest lines, go to either guild hall in your starting zone. For instance, if your alliance is The Daggerfall Covenant, you will pick up both quest lines in Glenumbra, finish the 2nd quests for each line in Stormhaven, and so on.

All of the DLC quest lines take place after both the alliance and main quest lines. All DLC quests can be started in your starting zone or from the crown store or from collections if you already own the DLC/ESO Plus.

NOTE: The Dark Brotherhood story arc should be finished before you take on Morrowind, and the Thieves Guild story arc should be finished before you take on Southern Elsweyr, due to a recurring NPC.

*Below, the DLC quest lines that contain vital story content will have an asterisk next to them, and I have separated them into story arcs. The major story chapters have the first quest name of the story line next to them in parentheses.

Dark Brotherhood (located in the Gold Coast)*
The Daedric Wars
Orisinum (Invitation to Orsinum)
Morrowind* (Divine Conundrum)
Clockwork* (To The Clockwork City)
Summerset* (The Queen's Decree)

Thieves Guild (located in Hew's Bane)*
Season of the Dragon
Wrathstone (Dungeon Pack)
Elsweyr* (A Rage of Dragons)
Scalebreaker (Dungeon Pack)
Dragonhold* (The Dragon's Lair)

The Dark Heart of Skyrim
Harrowstorm (Dungeon Pack)
Greymoor* (The Gathering Storm)
Stonethorn (Dungeon Pack)
Markarth* (The Despot of Markarth)

Gates of Oblivion
Flames of Ambition (Dungeon Pack)
Blackwood* (A Deadly Secret)
Waking Flame (Dungeon Pack)
The Deadlands* (The Celestial Palanquin)

Legacy of the Bretons
Ascending Tide (Dungeon Pack)
High Isle* (Of Knights and Knaves)
Lost Depths (Dungeon Pack)
Firesong* (A Sea of Troubles)

Shadow Over Morrowind
Scribes of Fate (Dungeon Pack)
Necrom* (Fate's Proxy)
Scions of Ithelia (Dungeon Pack)
Gold Road* (Paths of Chaos)

All other DLC quest lines can be enjoyed in any order, just so long as that order takes place AFTER the alliance and main quest lines. Those DLC quest lines are as follows:

Dragon Bones (Dungeon Pack)
Murkmire
Shadows of the Hist (Dungeon Pack)
Wolfhunter (Dungeon Pack)

Craglorn:
Craglorn is a PvE zone. The main quest line here is called "The Celestial Threat", most of which can be tackled solo. There are certain group areas which may require anywhere from 2 to 4 players, depending on skill level. The very first quest is "The Star-Gazers" and you can find the quest starter in Elden Root, Wayrest, Mournhold. His name is "The Star-Gazer Herald" and he will be next to a horse-drawn wagon that can take you there. Alternately, you can begin the quest line in Belkarth, or near Bangkorai Gate, from a bulletin board.

Imperial City DLC/Cyrodiil:
Cyrodiil is a PvP zone. Most quests have barely any story. However, it does take place during Molag Bal's Planemeld (the main quest) and before the White Gold Tower dungeon. You can enter this area beginning at level 10, when you receive the letter "Cyrodiil Awaits!" in your in-game mail. Upon entering, the game will apply buffs which allows you to play among higher-level players.

Other Dungeons:
Besides the DLC dungeons and the group content in Imperial City, none of the dungeons really have any impact on the main story line at all. All of the standard dungeons can be taken on just as soon as you unlock them.

Please use the following resources if you'd like to dive in even deeper. While my guide is intended to be convenient, simplified, concise, and easy to access from within the In-Game Steam Overlay, you will find the following resources to have greater detail (for better or worse) or perhaps a different focus than this guide entirely.

https://gtm.steamproxy.vip/sharedfiles/filedetails/?id=1826476600
The Unofficial Elder Scrolls Pages "Story Quests" Page[en.uesp.net]
The Unofficial Elder Scrolls Pages "DLC" Page[en.uesp.net]

Please let me know if you'd like me to expand on something or otherwise fix any errors. I'd like this guide to be as simple as possible, while also not leaving room for further questions that this guide should answer. Don't hesitate to leave a comment if you find something to be inaccurate or incomplete. Thank you :)