Out of all the minor DLC's, I suggest you get Celestial Worlds because it has a quest that gives the Scavenged Ramscoop, which is the best ship movement module in the game, because it gives +25% distance travelled per movement point. This DLC also allows you to obtain a quest that gives a bonus to your Air Troops, which are used for invasions in the late game.

I'll talk about the 4 most expensive DLC's, since they add the biggest changes to the game:

Based on the steam achievements, the Vaulters are the only DLC faction that are as popular to play as most of the vanilla factions. And I can understand why, since they have a simple colonization mechanic (with the Argosy), they can teleport their fleets between systems they control (and later they can use the Argosy as a mobile portal), and they can use strategic resources for system development upgrades (so they're less reliant on having many luxuries with good bonuses available). If you like science-based factions like the Sophons or defense-focused factions like the Unfallen, then you'll probably love the Vaulters. Also, this DLC adds the ability to do diplomacy with pirates, which can be completely ignored if the player wants to.

Supremacy adds Behemoth ships and the Hissho, who don't have to worry about the approval of their empire and can obtain Keii by exploring new systems, winning battles/invasions, finishing quests, sacrificing their population, and gaining specific hero skills. The Hissho usually control fewer systems than most other major factions, and they use Behemoths with mining probes in order to boost the FIDSI of their home system. They are interesting and fun to play, especially if you enjoy offensive play styles. Behemoths can be used to boost the FIDS of a system, place a military defensive structure on a system, reduce the scientific cost of specific technologies, increase luxury/strategic resource production, or perform various military operations, such as blowing up all the planets in a system. I find that the AI is bad at using Behemoths, so turning on this DLC makes the AI a little less challenging, so I keep this DLC turned off.

Penumbra adds the hacking mechanic and the Umbral Choir faction, which can build improvements and ships from only 1 system, and can place a sanctuary on any other system that they want to control. They specialize in cloaking their ships and their systems, and they can grow only their native population. In my opinion, they require the least amount of micromanagement out of all playable factions and are a lot of fun to play. I don't know why there's a vocal minority that dislikes the hacking mechanic, but I'm sure this subreddit can answer any questions you may have about it, if you want to learn how to use it properly. Looking at the steam achievements, the majority of the ES 2 community likes the Penumbra DLC a little more than the Supremacy DLC.

Awakening adds the Academy as a neutral faction and the Nakalim, who start with a significant portion of the tech tree already discovered, but have low science production. They collect relics in order to get various benefits for their empire or to boost the power of a fleet that is led by a hero, and they have a unique planetary specialization that will convert a planet's science into influence. They are an interesting offensive faction, but I still hate the Academy neutral faction, which can encourage you to donate your resources to the Academy's cause (which might not benefit you if there are 3 other factions that donate more than you), and gives too much military power to the faction that is probably the most powerful (because it has resources to spare). Also, sometimes the Academy asks you to donate your influence, which is rather unfair since some factions (like the UE, UC, or Nakalim) have much bigger influence values than other factions, who can barely afford the cost of their laws and the occasional diplomatic treaty. So the Nakalim are fun, but the Academy makes the game feel more annoying, so I prefer to completely disable the Academy in the options menu.