The first expansion for the original Destiny game was The Dark Below. Bungie released it on December 9, 2014, only three months after Destiny's September launch.
The expansion focused on the Hive and their powerful deity Crota, Son of Oryx, who had been mentioned in the base game. Its story followed the Guardian's efforts to stop the Hive from resurrecting Crota and culminated in the six-player raid Crota's End, set deep within the Moon.
The Dark Below added new story missions, weapons, armor, bounties, and Crucible content. It also raised the game's progression limits, giving players new reasons to revisit activities and pursue improved equipment.
The other options belong to later stages of Destiny's post-release history. House of Wolves was the second expansion, The Taken King was the third and larger expansion, and Rise of Iron was the fourth major expansion, released in 2016. The Dark Below is therefore the single canonical answer.