I don't know the differences between them, so I want to know which one I would get from the differences.
As bwDraco said, they are all different stories but there is more to it than that. Each campaign has a unique set of playable characters that can only be used in that campaign (most notable are the Hoshido/Nohr families from the game covers. They can only be used in their respective campaigns). There are a few serious gameplay differences between Birthright and Conquest as well. Birthright plays much more like Awakening, putting serious focus on the more "JRPG" aspects of the game - world map, level-grinding, more focus on shipping characters, and generally is played much more like an RPG than a strategy game.
Conquest, on the other hand, keeps to the series' roots much more strictly. From what I understand, Conquest is a linear progression through the story, meaning once you complete a chapter, you can't go back using the world map. Conquest is also more difficult as it is meant to be played much more like a strategy game than an RPG with strategy elements. If you're familiar with some of the older games, Conquest will be pretty similar to those. However, if you've only played Awakening, Conquest may be a bit of a shock at first at how different it is compared to Awakening.
To add onto Marth's answer:
All games are the same up until Chapter 6, when you are forced to make a choice. Conquest aligns you with Nohr, Birthright with Hoshido, but Revelations aligns you with neither.
Revelations is a blend of Conquest and Birthright, both story-wise, and gameplay-wise. You will be able to recruit almost every character available in Conquest in Birthright, which will unlock extra supports and 2 marriages per version-exclusive character.
In terms of gameplay, the campaign is less difficult than Conquest, but more rigorous than Birthright. From personal experience, I believe the difficulty of Revelations is closer to Conquest, but you are able to train your units on previously completed maps, similar to Birthright.
In your Castle, you can have buildings from both games (i.e. you could produce both ruby and coral, or buy tomes as well as staves).
It is worth noting, however, that it is intended for the player to at least play either Birthright or Conquest before playing Revelations.