FIRST:
> children record

SECOND: any character songs - watch in any order i guess? it doesn't really matter. mekakushi code is probably a good one to start with tho
> mekakushi code
> kisaragi attention
> yobanashi deceive/night tales deceive (read note below for this one - both titles give you separate translations for the PV and i prefer the former but it doesn't really matter i guess)
> ene's cyber journey - EXC
> *imagination forest + shounen brave - EXC (coincide w/ one another - probably best to watch last since it's also 'storyline'-ish)

THIRD: storyline songs - some are also technically character songs but. stick loosely to the order i write
> jinzou enemy
> *kagerou days
> headphone actor
> sunset yesterday
> konoha's state of the world (somewhat coincides with kagerou days)
> otsukimi recital
> *ayano's happiness theory
> *lost time memory
> transparent answer - EXC
> dead and seek/gunjou rain/shinigami record - all EXC (probably just generally a good idea to watch them w/ each other - provide background on some not main characters that are still v important)

FOURTH: ending songs
> *outer science
> mary's fictional world - EXC (sort of a 'sequel' to outer science)
> *summertime record

_______________
THINGS TO NOTE (i copy/pasted this straight from my previous list): if a song says EXC next to it, it means that song is an exclusive or 'bonus' song, per se, and only two of the seven exclusive songs have PVs to accompany them so don't worry if all you see on the screen is lyrics. an asterisk (*) means the song is, in my opinion, one of the most important songs in the series, so pay super close attention to those. also there's a lot of songs that are hard to understand even if you look up the meaning on the song's wiki page (kagerou days, lost time memory, outer science most notably) so there's also this masterpost that will give you explanations for any song you need:
http://vgperson.tumblr.com/post/24422453954/jin-jin-summary-yo
(albeit some of the song titles are different)
but yea the series is still confusing af ??? there's still shit that even i can't explain but i can PROBABLY answer any question you have so. yeah. also the names for the songs listed are the ones you can take verbatim and type into youtube and the first result should be the original PV you're looking for, though that doesn't mean that's the only name the song has or even the preferred name (like ayano's happiness theory is what u have to type in for that PV but the title is technically ayano's theory of happiness? it's not a big deal but i prefer the latter so ehh)

so yeah! happy kagepro-ing friend 8)