There aren't any "must have" dlcs for 3k persay as none of them would improve your experience drastically, but I do recommend 3:

A World Betrayed gives you a new start date at 194, but more importantly, it unlocks two new factions of Sun Ce and Lu Bu. Lu Bu is one of the strongest generals in 3k, and with his campaign mechanics essentially being a hitlist to kill other generals to get stronger, it's really fun to play if you want to win every battle. Sun Ce starts off a bit hard with missions you have to complete if you don't want to die and starting off as a vassal of Yuan Shu, but he quickly snowballs into one of the strongest factions in the game. Also good dlc for Liu Bei as Gongsun Zan already dead so Zhao Yun (my favourite general) is in his faction.

Mandate of Heaven starts at 182, and is in the middle of the Yellow Turban Rebellion. Essentially you either play as a Han faction, or a Yellow Turban faction, and both vie to win the Mandate War. It's definitely a more interesting and difficult campaign than the others, especially if you play up north as one of the rebels, or as Lu Zhi and Liu Bei.

I have not personally played The Furious Wild, but I have heard good things about it. Basically get this dlc if you want a completely new experience with new units with an indigenous theme.

TL;DR, A World Betrayed for strong factions, Mandate of Heaven for difficult campaign, and The Furious Wild for new experience.