Yeah I would say the DLC for ME3 make it better overall experience (which is a little infuriating because you have to pay extra for some of the best stuff). I would say you should definitely get Citadel, Leviathan and Javik (whatever his DLC is called). Citadel is one of the most enjoyable parts of the game. It's more light-hearted than the rest of ME3, but it's EXTREMELY satisfying. Leviathan is intense, adds a lot to the story and has some good character beats too. Javik makes the game MUCH better as he adds lots of information and a completely different perspective to the crew (NOTE: Take him and Liara with you on Priority: Thessia). Omega DLC is more iffy. It has really good gameplay, probably some of the best in the entire series, but it doesn't add anything to the story overall IMO.
I would love a DLC to ME3 that points us in the direction of ME4. I doubt they will do it at this point as they will want the first foray into the new series to be the main game itself.