There's a not-yet-scanalated, 13-volumes long prequel. Do I have to read it first to appreciate this story fully, or do I need to know of some particular information?

My current top 3:
Fullmetal Alchemist
Pandora Hearts
3-gatsu no Lion

The manga is not exactly a sequel, it's more of a spin-off type of thing. I read started reading Discommunication Seireihen without even knowing about Discommunication, and had no problem following the story, by the time Seireihen was scanlated two chapters of Discommunication were out and they did had a bit of background on the characters but it wasn't strictly necessary, especially since the translator of Seireihen did a very good job and added many useful notes to his translation that explain what you need, and Discommunication seems to be very episodic, so you are not losing any earth shattering revelation.
In conclusion read the three available chapter of DIscommunication to get a bit of background on the characters and then go on to Seireihen without fear.

Exactly as Topomouse said. The original story was pretty episodic anyway, so there was no overarching plot and it actually got pretty repetitive halfway through. Discommunication Seireihen is a concise version of the prequel, and therefore more interesting and to-the-point, imho.

I see, thank you!

My current top 3:
Fullmetal Alchemist
Pandora Hearts
3-gatsu no Lion