I left the game just before it went F2P and now I'm back and have just finished the class story for a new character (i.e. up to the beginning of Interlude). I'd like to explore the added content now, but unsure what the order is. This is what I have available as quests:

Ilum: Crystal Ball

Makeb: Trouble in Paradise

Oricon: Day of Dread

Macrobinoculars: The Shroud's Gambit

Shadow of Revan: Forged Alliances: Part I and Prelude

Seeker Droid: Master Gand's Mission

Then of course I have Fallen Empire on my ship's mission console.

I basically want to do these in order that the content was released, but I don't know what that is.

Ilum: Crystal Ball

Makeb: Trouble in Paradise

Oricon: Day of Dread

Macrobinoculars: The Shroud's Gambit

Shadow of Revan: Forged Alliances: Part I and Prelude

Seeker Droid: Master Gand's Mission

 

I basically want to do these in order that the content was released, but I don't know what that is.

Ilum is the end game of the original game - essentially what you are doing during the interlude. Next is Makeb. The Macrobinoculars and Seeker Droid quests were released during the Makeb expansion (RotHC). Oricon is between Makeb and Shadows of Revan and of KOTFE is the current. Note that the is a Prelude to Shadow of Revan that is available from your ship terminal. It fits between Oricon and SoR.

Personally I never did Ilum. I just came back and went from the end of Makeb into the Shadow of Revan. I just hit 62 on Rishi still with plenty to do for SoR - the double exp is insane.

At least I think that is the order... I'm sure someone will correct me if I'm wrong

If you're in a rush, the core single-players stuff is Ilum -> Makeb -> Forged Alliances Flashpoints (you can select solo-mode for all of them) -> Rishi / Yavin -> Ziost -> Knights of the Fallen Empire.

Oricon can be considered a 'core' story arc (between Makeb and Forged Alliances), but be aware it requires running two Operations to complete the quest line.

Here's a list of the post-50 content in chronological order. Make sure you have the "Show Exploration Missions" option toggled On on your map screen or else there will be some missions that aren't available. (Some of the references to Operations being Level 55 or whatnot are now out of date since 4.0 changed how end-game Ops work - but the chronological order still stands.)

Here's a list of all the post-Class Story storylines, based on the chronological order that max-level content was released (which seems to track the in-universe progression). The game does not allow you to enter an Operation without an Ops Group formed, but you can make an Ops Group with as few as two players and Eternity Vault and Karagga's Palace can probably be cleared with two level 60s at this point:

 

The Cold War and the Start of the Second Great Galactic War

• Class & Planetary Quests up through Corellia and the end of your Class Story plus Flashpoints as they become available (all Flashpoints have one-time quests that can be picked up on Fleet as soon as you hit the level for that Flashpoint and most of these quests can also be picked up on the level-appropriate planets)

 

Ilum and the New Empire

• Ilum Planetary Quests (starts with quest you should receive automatically once you finish your Class Story)
  
• Battle of Ilum Flashpoint (continuing the Ilum quest line)
  
• The False Emperor Flashpoint (concluding the Ilum quest line)

 

The Return of the Infernal One

• Eternity Vault Operation (one-time quest picked up on Fleet)

 

Prelude to the Hutt Cartel Conflict

• Karagga's Palace Operation (one-time quest picked up on Fleet)

 

The Rakghoul Plague Outbreak

• Kaon Under Siege Flashpoint (one-time quest picked up on Fleet)
  
• The Lost Island Flashpoint (concluding the one-time quest that started with Kaon)

 

The Black Hole Crisis

• Black Hole Daily Area (one-time quest picked up on Fleet starts the progression)

 

The Dread War Begins

• Explosive Conflict Operation (one-time quest picked up on Fleet)
  
• Terror From Beyond Operation (one-time quest picked up on Fleet) [because this Operation has been adjusted to level 55 it's worth noting that nothing is glaringly out of order if you do this after Makeb, but it should be done before Scum and Villainy]
  
• Section X Daily Area (one-time quest picked up on Fleet starts the progression)
  
• HK-51 Quest Line (starts with quest picked up in Section X)

 

Conflict with the Hutt Cartel

• Scum and Villainy Operation (one-time quest picked up on Fleet) [because it is a level 55 operation, this is something you'll probably end up running after Makeb. Other than a single line of dialogue on the Republic one-time quest (response to "But their leader is dead!" dialogue option), nothing is badly out of place if you do this content after Makeb. This Operation also ties in to The Dread War storyline and should definitely be run if you want to experience that full story.]
  
• Makeb Planetary Quest Line (starts with quest picked up on your ship's holo-terminal)
  
• Shroud (Macrobinoculars) and Seeds of Rage (Seeker Droid) Quest Lines (each starts with a quest that can either be picked up on Makeb at around the halfway point of the planetary quest line, or on the Fleet once you hit level 52)[seeds of Rage questline also ties in to The Dread War storyline, should definitely be run if you want to experience that full story]

 

The Fall of Czerka

• CZ-198 Daily Area (one-time quest picked up on Fleet starts the progression)
  
• Czerka Corporate Labs Flashpoint (continuing the CZ-198 one-time quest)
  
• Czerka Core Meltdown Flashpoint (concluding the CZ-198 one-time quest)

 

The Dread War Ends

• Oricon Planetary Quest Chain (starts with quest that can be picked up either on Fleet or CZ-198)
  
• Dread Fortress Operation (continuing the Oricon quest line)
  
• Dread Palace Operation (concluding the Oricon quest line)

 

Forged Alliances

• Assault on Tython and Korriban Incursion Flashpoints (order is determined based on your faction, one-time quest picked up on fleet)
  
• Depths of Manaan Flashpoint (quest to continue the progression picked up on fleet from same droid who gave part I)
  
• Rakata Prime Flashpoint (quest to continure the progression picked up on fleet from same droid who gave parts I and II)
  

 

Shadow of Revan

• Rishi Planetary Quest Line (starts with quest picked up from Forged Alliances Droid on Fleet or from terminal on your Ship)
  
• Blood Hunt Flashpoint (Rishi Quest Line directs you to it)
  
• Battle of Rishi Flashpoint (Rishi Quest Line directs you to it)
  
• Yavin IV Planetary Quest Line and Daily Area
  
• Temple of Sacrifice Operation (one of two options for how to finish the Yavin IV Quest Line)
  
• Ravagers Operation (one-time quest outside the Operation entrance on Rishi) [separate from main quest line with stand-alone plot, can be done anytime after you hit 60 and have been to Rishi]
  

 

Rise of the Emperor

• Ziost Planetary Quest Line (starts with quest picked up on fleet)
  
• Ziost Daily Area (planetary quest line leads into it)
  

 

Knights of the Fallen Empire

• On-Going Quest Line [Chapters 1-9 currently available] (starts with quest picked up on your ship)
  
• Star Fortress Flashpoints (on-going quest line leads into them)
  

With 4.0, the 'breadcrumb' mission to Section X (part of the Dread War arc) seems to be missing, not sure if that is a bug (I hope it is) or if they just pruned it out. All the missions in Section X are still there, though, so you can still complete those and can still get HK-51, you just have to head directly to Section X instead of picking up the "go there" mission from the Fleet.