Everyone has their own recommendations for what order to play the routes in, here's what I recommend and why
Prologue --> Reina --> Elle --> Sylvia --> Akane --> Ria(True Route) --> Prologue --> Sylvia(a little bit extra post credits content unlocks if you replay if after completing Ria's Route, also if you hit the extra button afterwards you'll see a little slideshow that includes a new image.)
Every route covers a slightly different aspect of what it means to be golden(a japanese colloquialism for the word ideal), while also fleshing out different aspects of the game's world and the backgrounds/personalities of the various characters.
Prologue
-Note1: (It'll probably feel super cringey and over the top unrealistic at first in large part due to the MC's thoughts(aka: wrong impressions) as events take place but it'll get better a little after the incident involving water being spilled on his backpack(takes place fairly early on.)
-Note2: (Anyone that enjoyed the game should play this portion again after having completed every route it's designed in a way that makes it far more enjoyable if you already know everyone's personalities/antics, compared to if you're getting to know everyone for the first time.)
-What it does: establishes the setting, a basic outline of what the characters' personalities are like, and a couple of conflicts, by the end only two conflicts remain, that a particular noble girl is probably still out to get you, and the stuff regarding why you dropped out of your old school.
Reina(princess's friend)
-what it does: Naturally transitions on from the prologue, properly addresses both of the conflicts from the prologue, fleshes out the personality of the girl the route is about and, the personality of the mc's former friends, Also lightly fleshes out the personality of the noble girl that was out to get you in the prologue. Also addresses how the princess feels about the mc falling for someone other than herself.
Elle(princess's personal knight)
-What it does: Starts off in a way that would feel very unnatural if you haven't completed atleast one route, and eases you back into the feeling of being just friends with Reina, gives you a bit of background regarding the princess's homeland particularly it's politics. Addresses the issues pertaining to what would happen if the MC fell for someone from the princess's group, fleshes out personalities basically everyone related to the princess to some extent. As well as the relationship she has with everyone surrounding her.
-Note: super cringey early on but better as it goes, in this instance though it doesn't get better upon later playthoughs(since the issue is that the security people are weirdly stupid for a while, for the sake of getting the ball rolling on the story.)
Sylvia(the princess)
-what it does: gives another side of the story in regards to the main conflicts that takes place in of both of the prior routes while informing you of the princess's feelings in regards to both matters(the reason it's best not to play this until you've played through the first two), fleshes out the relationship the protagonist has with his family, the kind of relationship the princess and ria had as children, and the relationship their whole trio(sylvia,ria,ichi) had as children. Also fleshes out the relationships the princess has with her family, and the relationship the protag has with mina.
Akane(the mascot character, only route unrelated to the princess, basically the MC except female)
[unlocked by completing a single route, better the longer you wait to play it, since although it cannot spoil anything or be spoiled by anything, it relies heavily on your knowledge of what the protagonist is like to be properly appreciated.]
-What it does: help's you understand why the girls fall in love with the protagonist inspite of his clear and obvious faults and why they still consider him "cool", by having a girl that is basically what the protagonist is described as being like by every girl he pursues in every route leading up to this point, pursue you instead. The more routes you've played while paying attention to MC's antics/personality, the clearer the comparison becomes, and she even gets her own what it means to be golden segment where she aims to better herself as the route goes on and you get to be the partner that helps instead of the one being helped.
-Important Note: Unlike the other three routes this one doesn't revolve around the player's relationship with the princess in anyway and doesn't really give you anything new worldbuilding wise, or even bother with fleshing out any unrelated characters. It's primary purpose seems to be to let the player understand the mindset behind devoting yourself entirely to ensuring the happiness of someone you love dearly, and loving someone simply because of how brightly they shine. [The fact that this entire route is basically entirely devoted to getting you to better understand Ria's mentality in order for you to better appreciate the true route(ria's route) is the reason I advocate for this one being the one you play right before playing the true route.]
Ria(The True route)
[unlocked by completing every other route, amazing if you've experienced all other routes not so much if you haven't, basically do not download someones save file and go straight to this or skip through the other routes and expect to understand/appreciate this route]
-What it does: actually goes into proper detail in regards to what happened in the past and why the protag lost(repressed) his memories of the past, properly fleshes out the personality of ayaka(prologue girl), the main girl(ria), and gives ria's perspective on a lot of stuff, explains why she gets frustrated when the protag calls her his favorite guy friend or is openly dismissive of her as a girl despite not making any effort to get his attention, why ria has resigned(committed) herself to getting the protag and the princess together, etc.
Lastly just somethings people that have finished the game might like to be aware of(nothing that can ruin anything even if you haven't played it yet.)
This game has a sequel(fandisk) that is currently being translated maybe keep an eye on that, also here's a fun bit of trivia: there's a question that constantly gets brought up in the story but never resolved, where did the box come from, there's legend that you get told bits and peices of in every route that never seems to really be relevent about a time paradox in which tossing an item into the lake with thoughts of helping a loved one can change the past because god will intervene, and the start is about how the protagonist was suicidal and saved thanks to a friend he made years ago thanks to the box, most likely Ria would've found out if something happened to the protagonist via the protag's family and been the one to toss the box into the lake, an original timeline that takes place before this game takes place, and in the true route it ends with the protagonist tossing the now slightly altered box into the lake with similar sentiments and his past self discovering it, likely causing a slightly different miracle to transpire as well. This game is about Ria's wish, and the fan-disk seems to be about the protagonist's wish.
