I Suggest Dallan route since is the most complete and obviously no spoilers but it will have a huge plot twist that would make understandable any future interactions with the trio. In conclusion I can tell you since I played (still playing) this game a lot that:
Tate route is full of emotions, the history about the academy, the previous headmaster and overall the relationships that the leaders have between one another
Dallan route is a peaceful and wholesome journey with a plot twist a the end, it does also have some lore but you need to dig bit for this one
Aiden route is romantic, complicated and show us the headmaster's future plan and how the test will work but the route it's gonna be rewritten soon, so yeah
Scribbles route (counting also Alvy and Therium) it's the most intriguing and cryptic story of the bunch and all I can say is that this route will make extremely more sense if played last