To describe the songs in the Kagerou Project, I would say they are like a spiderweb. Each song tells about an event or a story involved some characters that seems like they don't have much relations with the other songs, but in fact each song contribute something to the big picture.
I personally think you should listen to the order of songs in according to the tracklist from Jin's two albums, Mekakucity Days and Mekakucity Record.
If you want to listen to a more linear order of songs, you can refer to my recommended order below. I categorized the songs into storylines as what I think as a coherent order to view the songs. All of the official PVs are made by Shidu and Wannyanpuu, some PVs below are fanmade.
Spoiler for Kagerou Project recommended order:
1)
Project Opening Theme:
Children Record
2)
Mekakushi Dan storyline, contains songs that tell about the current timeline on how all the current members got involved and joined the Mekakushi Dan:
3)
Yuukei Quartet storyline, contains songs about the quartet Shintarou/Ayano/Ene/Konoha:
4)
Other character-centric songs, which help in explaining some of the big mysteries of the series:
5)
Ending:
Outer Science ->
Mary's Fictional World (fanmade PV)
6)
Project Ending Theme:
Summertime Record
Extra: There are also 4 voice clips which are the exclusives in the 2 albums Mekakucity Days and Mekakucity Record (Lost Time Prologue, Kaien Panzermast, Summer Endroll and Crying Prologue), all have been translated
here
If you don't like Vocaloid, then
this playlist might be for you. In the playlist I included all the Kagerou Project song covers which are to my liking. I also listed engsub vocaloid Kagerou Project songs that have no covers or have non-engsub covers. Notice the notes under the video's name to know which songs are Vocaloid and which songs are English subbed.
Feel free to discuss with me about any changes that should be made to this guide.