Honestly, I would say do everything.
Keep an ear out for Traynor (ME3's version of Kelly Chambers). She will tell you about some side missions, which are time sensitive, and need to be done to recruit back (and make sure they don't die) some of the ME2 cast. The game doesn't tell you that these missions have a deadline, so I would recommend to do these as soon as you unlock them.
EG, no too far into the game Traynor will tell you about a mission in Grissom Academy. It has nothing to do with the main story, but you will meet one of your ME2 squad mates here ... and if you leave this mission idling while doing the other story content, eventually this mission locks out and that squad member dies in the background.
Here's how I would space out the DLC for optimal experience:
- From Ashes (The DLC mission for Javik, the Prothean party member)
Do THIS ASAP. Javik is essentially a mandatory party member. Bring him in any mission that may involve Asari for optimal lore.
Or hell, just bring him in every mission to see how everyone reacts to a living Prothean. It's pretty fun actually.
- Leviathan DLC Missions
These missions unlock some ways into the game and they give the most back story on Reapers.
You can do these any time in the later parts of the game once you feel like you're getting closer to the final stretch.
The DLC pack is divided into a half dozen or so story missions, so you can even do one of the story missions for the DLC in between the regular story missions to spruce it up.
- Omega DLC
This is a long single continuous mission. Not my favorite, I just get it over with as soon as it becomes available.
- Citadel
This unlocks in the 2nd half of the game and IMO is the *true ending* of the game, even though it takes place before the story ending.
This is the final DLC ME3 got and a big love-letter from Bioware. Every character is present, including all the cast from ME1 and 2 (Wrex etc).
My recommendation honestly is to leave this until you beat the story for the maximum effect and enjoyment. Doing this before you finish the the the first time will just make the regular ending seem that much plain and meh.