There's a walkthrough in the OP.
But it isn't necessary to take the concept of "days" into account as you won't lose out on any content by making the time advance or skipping weeks unless you are in debt or in some specific quests where your debt will grow as time passes.
You asked for an 'optimal walkthrough' to which I get you want to get the most content in a single day but uhm... I guess getting some levels first would be good. In my case, I always do Kate's quest first because as you advance then you can work for her mother who will also give you some soup to regenerate the food bar. And I don't really remember if this was removed or if it's still there but I think if you advance with Kate's love route and play the tavern minigame she'll give you the day's earnings.
Because I always play quests as they come I don't really have a 'useful' advice so take this more of an opinion than an actual tip.