Assuming you don't want to cheat I would recommend to be able to generate some money early on. That would be to learn cultivating from Daisy as a first thing, as that will unlock Douie and you can then help there (morning and afternoon). This gives you another option to earn money.
It's also good to learn milking from Anna, as you can sell some milk later to Pixie. The Anna questline is also a very long one, so you might as well give it a little head start,
So is there no real advantage to attending class at school except for perhaps on Fridays to take the weekly exam that day other than interacting and gaining relationship points with everyone at the school as long as you are studying at home periodically?
I've been going to school M-F and not working helping Carter in the mornings because it conflicts with attending school but can you help Carter to earn much needed money early on in the game and not really hurt anything school wise if you just started attending regularly there until say like Week 3?
We don't really learn any skills while at school so it does seem like kind of a waste to spend any time in class. Can you obtain any special items that really help in the game by someone at the school possibly that really makes it worthwhile building relationships there?
There are several quest lines and relationships/characters that require you to go to school. The school is quite an important part of the game, but you will not get punished if you skip it sometimes.
You can help Mr. Carter in the morning if you get up early and go there directly. Then you can still attend school. I played the game that way that I saw school as the main job and attended it whenever possible. But there are some things that require you to skip school if you want to progress there.
I hate that part that talking to Corona will force you to fail school on that day. How long can a short chat with the post box take?
