This Old Waystone

Extra action button, not interactable object. Don't be a silly head like me. :)

On a quite new character, I had to do some of the old campaign quests (2/9) until helping to free the Runecarver's arm. I got The First Move when I turned in The Weak Link and returned to Oribos.
You can talk to Highlord Bolvar Fordragon instead of [npc=177136] to skip until Korthia.

When I skipped it, I immediately got Call of the Primus. Talk to Tal-Inara in Oribos to start the questline for Zereth Mortis.
She also offers a skip, I've you have done the campaign with an alt before. You'll start there with 3/7 chapters of Secrets of the First Ones and unlocked world quests.

Beware that you will miss the rewards of the first three chapters, if you skip them.
Edit: With the Hotfix for March 18th, players who skip the Zereth Mortis story will get the reputation with the Enlightened.

Campaign:
Chapter 1

1. 
   
2. Call of the Primus - Talk to [npc=159478], turn in at [npc=181655] after that
3. 
   
4. A Hasty Voyage - click [npc=182607] behind you. Click [spell=361417] and [spell=361571] to fill the bar. Don't skip the cinematic
   click [spell=368613], [spell=368614] and [spell=368621] to match the emotes.
5. 
   
6. Long Lost Firim - find Firim and click the 4 objects
7. 
   
8. Give Me A Hand - follow [npc=181561], click the door, then [npc=184057] and defeat [npc=184058]
9. 
   
10. A Mutual Exchange - go to south, step on the teleporter and click your extra button [spell=365986]. Kill [npc=184860] and loot the core
    For Research Purposes - collect 12 items
11. 
    
12. The Road to Haven - mount [npc=184082]
13. 
    
14. Forging Connections - go to Haven, talk to [npc=177486]
15. 
    
16. Defending Haven - kill 13 enemies
    Destroying the Destructors - destroy 4 objectives
17. 
    
18. This Old Waystone - follow [npc=178016] to the cave. Stand in front of the waystone to get the extra button [spell=367326]. Click the stone, turn in in Oribos
19. 
    
20. The Forces Gather - return to Zereth Mortis and talk to [npc=177486]
21. 
    

Chapter 1 took about 25 minutes with itemlevel <190.

Chapter 2:

Spoiler

1. 
   
2. Favor of the First Ones - burn 8 objectives
   Necessary Harvest - collect 15 protein from enemies
   Our Forward Scouts - find and talk to 3 [npc=185844]
3. 
   
4. Knowing is Half the Battle - travel to the marked area, meet [npc=181180]
5. 
   
6. Scour the Sands - go to the yellow circles to discover the area. If you lose your stealth, talk to [npc=181180] nearby
   /way 48.43 47.54 1
   /way 51.51 48.59 2
   /way 50.60 45.25 3
   /way 47.99 44.84 4
7. 
   
8. Battle for the Forge - kill 8 enemies
   Together, We Ride - click 5 [npc=181429]
9. 
   
10. In Plain Sight - reach the obelisk and kill enemies behind you until [npc=182357] is attackable. Kill it
11. 19 minutes
    
12. Reinforcements May Be Necessary - return to Haven
13. 
    
14. A Break in Communication - give orders to 3 NPC
    Nothing is True - kill 4 [npc=181884]: throw questitem [item=187839] on [npc=181884]
    This is Your Fault, Fix It - click 5 [npc=181339]
15. 
    
16. Doppelganger Duel - go to the marked area in the middle of the map and fight against this person :-)
17. 
    
18. Fighting for the Forge - talk to [npc=183724]
19. 
    
20. Seeking Haven - click the teleport to return
21. 
    

Chapter 2 took about 40 minutes with itemlevel <200.
I got several itemlevels, about 1900 rep with [faction=2478], some Anima and 12 renown so far (chapter 1 & 2).

Chapter 3:

Spoiler

1. 
   
2. Danger Near and Far - go to the marked area and enter the building
3. 
   
4. A Mysterious Voice - click the door, watch dialogue and kill attacking enemies
5. 
   
6. Core of the Matter - return to Haven and talk to [npc=177486]
7. 
   
8. Seeking the Unknown - enter the building at 33.63 65.78 and click the information
9. 
   
10. Finding Firim - find the NPC, click its corpse and go to the cave
11. 
    
12. Security Measures - click the [object=373576] near you. Leave the cave and reset 10 traps
    Unseen Agents - kill 3 enemies
13. 
    
14. Now You May Speak - talk to [npc=177958] and click the console
15. 
    
16. Surveying Cyphers - examine the 3 concordances marked on your map. Visit the fourth location. Kill [npc=179939] and click the item behind him. Return to the cave
17. 
    
18. Cyphers of the First Ones - click the console again. Unlock the first option and get your Pocopoc
19. 
    
20. The Way Forward - return to Haven
21. 
    

Chapter 3 took about 30 minutes with itemlevel 200. It gave less rewards than the previous ones.
In total I got about 2k reputation, 15 itemlevels and 15 renown.

Accept [quest=65324] before you go on with anything.

This is the quest that actually unlock the Anima Reservoir (NPC where you deposit Anima) and the Forge of Bonds (to swap Soulbinds and/or conduits), both from within Zereth Mortis.

The Anima Reservoir is at Zereth Mortis: Haven (34.86, 65.88) near the lake, and the Forge is at Zereth Mortis: Haven (35.19, 63.99) near the Inn. Same places for those characters you chose to skip the first 3 chapters (this os the second to last quest of the first one).