Mass Effect 3 DLC:
Citadel: The ultimate fan service. If you like your squad mates, you'll definitely want to pick this up. It's quite lengthy as well and even has battle arenas where you can team up with any squad mate alive from ME1 - ME3. It's considered to many as the "true" ME3 ending.
Leviathan: This one is the most meaningful in terms of story. It has investigation elements in it as well. It's very well done and in my opinion, it's important enough to be in the vanilla game.
Omega: This DLC is action-packed and FUN. The main reason you read people complaining about it was the price point. Well now it's the right price so go for it if you like action, Omega, Aria, or an interesting antagonist.
From Ashes: The most important dlc, story-wise. This one definitely should have been in game. Javic is one of the funniest party members to have and the recruit mission is nostalgic for anyone who has played Mass Effect 1.
So if you're looking for story: From Ashes and Leviathan.
If you're looking for fun: Citadel
If you want non-stop action or have Aria fetish: Omega.
But the ME3 dlc going on sale is so rare, you mind as well just buy all of it.