I would say From Ashes, Citadel, Leviathan, Lair of the Shadow Broker, Overlord and Prince of Revenge. Those are what I think.
For me, it’s hard to have the third game without Javik, but he’s not required. Citadel is a good one if you’re looking for a laugh and need a break from all the reapers. Leviathan drops some heavy lore reveals and it was a lot of fun to play through.
Overlord is not required either, but I really liked it because of the payoff in the third game (at least for me) the payoff is small and not very revolutionary, but I’d be lying if I said I didn’t almost cry.
Lair of the Shadow Broker is just fun as hell. It’s also not required really, but it’s my favorite dlc in the second game. You also get access at the end to intel that can leave you rolling in resources you need for the suicide mission. The boss battle is also creative and I found really fun.
Prince of Revenge, not required, but it’s free and Zaeed’s is a pretty cool character.
I like Arrival, but it doesn’t really effect the third game all that much except for new dialogue you don’t get otherwise. It gives context on how Shepherd ended up under house arrest, but that’s pretty much it.
Anyway, those are my recommendations.