Best ME3 Story + DLC order?

Omega early, before the Citadel coup, which means before Priority:Tuchanka.

Leviathan can actually be spaced out, as you return 3 times to the Citadel to advance it. I usually do it mid-game (i.e. post Citadel coup).

Citadel DLC can't start before you did the Citadel Coup and it comes in 2 parts. The 1st section has a storyline that you need to play all the way. The second section with the party/squadmates Silversun Strip activites allow you to leave the area and come back. So you can do the first part early and the party right before the ending.

My opinion: for story cohesion, the Tuchanka and Rannoch arcs convey a sense of urgency, even though they are not really urgent at all (you do not lose war assets and there is no visible death tally if you delay in completing in these arcs). So if you want to maintain that sense of urgency I would not do the DLC missions while you are in the middle of those story arcs.

So basically, do DLC before or after starting these story arcs.

Generally for new games, I recruit Javik right away to maximize his dialogue. I will go to Bryson's office early since I do all the early Citadel stuff for quick credits and XP and quests and whatnot, but do not do any missions until after Tuchanka. The order in which I do things is different per playthrough. I will save the Citadel DLC party until the very end, just before going to Cerberus HQ.

For NG+, I make a beeline for 10% store discount, so I do all the DLC after the Ardat Yakshi Monastery (unlocks after the Citadel Coup) to maximize my spending.

Why would someone want to wait to bring Ashley to unearth Javik? Does she have some kind of noteworthy lines? If so, I'd just watch them on YouTube.

Javik is a way more important character in ME3 than Ashley. I'd never delay his addition, and all his input, just so she could tag along. (To be honest, I'm not a fan of ME3 Ashley, and generally give her an honorable exit on Virmire. I think ME3 Ash is "airlock" material, as Javik might suggest. 😄)

From Ashes after Menae because Lord Javik is crucial. Would do it before but you can't even bring him there.

Omega early to get all the weapons and mods. New game I generally wait until just after the Coup so I'm sure to have enough to buy everything.

Leviathan and Citadel after Rannoch so I have the full squad available for dialogue and interactions.

I just use Multiplayer promotions to up the N7 Special Ops war asset to the point where I can get the line at the very beginning.

Obviously can't do that in the LE. 

I find that Omega fits best post Citadel coup, as a kind of payback to Cerberus. By that time i also have resolved most/all of Arias requests and the stuff EGM adds to the questline.

I believe i usually start Leviathan shortly thereafter - post Asari monastery, as that one introduces Banshees. Then the rest is spaced out, so that the last mission is post Horizon, pre Citadel Party.

Oh, right forgot about that. There are some LI lines in Leviathan and you fight banshees. Wouldn't make sense to start Leviathan before the Ardat-yakshi mission.

^^^ All of that.

I prefer CEM. Citadel DLC is best experienced as a post-drama situation.

Eventually I plan on modding it substantially, minimizing interaction with Brooks to the point where she is barely there. Most annoying DLC character they have ever made.

Good reasons.

I don't often have Ash alive in ME3, so the obvious wish to bring her full circle had flown right over my head. Duh. Different observations from Javik would likewise be cool to see.

For me, I enjoy his cheery, upbeat presence too much to leave him for so late in the game. He regularly makes me both laugh and feel badly for him. He's also very useful in combat, particularly for powers-focused Shepards.

I will have to visit YouTube tomorrow to check for videos showing both Ash returning to Eden Prime and Javik having a more positive assessment of the situation after reading Shepard's experiences. I typically recruit him straight out of the gate, so I've never seen these circumstances.

Even with the crappy endings (IMO), the myriad variables they accounted for in these games, particularly ME3, is so impressive. It makes the series unique. There is nothing quite like it, and likely never will be again. It's a ton of work for a limited payout.

If everyone played like themikefest and tried to experience and appreciate the variance, that would be rewarding for the devs. Most never do, though, and all those resources and hard work never pay off in those cases.

When he first grabs Shepard on the ship. If ems is high enough, he will say you believe you are winning. Of course if ems is high enough before the coup or the genophage, he will have that comment. It depends on the amount of assets collected when he's recruited. With the remaster, I haven't figured out what the cutoff point is yet. 

The last mission of Leviathan should be done after Thessia.

I usually do From Ashes and Omega fairly on as in during thr Turian Krogan arc Leviathan aroumnd midgame after the Citadel coup whils tworking through the Quarian/Geth par tof the game and Citadel during the endgame. Though given the way a lot of the DLC weapons are locked now in the game and the fact you have to buy them you may want to start Citadel earlier in order to earn credits from the Arena but that's up to you.

This is how I'm planning omn doing it in my current run. Also how I tend to normally play it.
Surkesh
From Ashes
Grissom Academy
Omega
the rest of the turian/Krogan arc
Citadel Coup
Then I tend to mix up Leviathan in with doing the Asari quests aqnd the Quarian/Geth arc as for exactly what order this can changeI fi decide to open up Citadel DLC early like I hav ein m ycurrent playthrough then I also mix this up in there as well. I always save the Citadel party though until I'm ready to start the finale.
After the Quarian/Geth arc then obviously Thessia and Sanctuary.

If I haven't started the Citadel DLC yet and I plan on playing it tthen this is when I will and do it all in one go. If I've only go tthe part yleft this is when I'll have that. After the party then comes the finale