For the most part I suggested the whole class thing because whenever there's a school setting and no one knows who's with who things end up being too chaotic. As to how it's important to the plot It's not really that essential other than solidifying the school aspect of the story. For the most part I think we won't dwell too much on the classes, but since we are in a school setting they are important.
i agree with Athos in that schedules should be blocked so that at least everyone has the chance to meet with a character outside of their little groups, this way the whole "I bumped into you for no good reason" situation is avoided. If I remember correctly in the HP world core classes are divided among the houses so two houses share the same class with the same proff at the same times, while they have another class with a different house. This applies to all core classes, and major subjects. The only classes that don't follow these rules are the electives, i believe.
For the classes themselves there are seven core classes in the HP lore, Transfiguration, Potions, Charms, Herbology, Defense Against the Dark Arts, History of Magic, and Astronomy. Now in the RP we have four extra classes in the story, Oriental, Voodoo, Natural Arts, and Shamanism. That makes up to at least 11 possible classes total, and the various electives.
Within the HP world not everyone is required to take all seven core classes when in their later years. Lets say that in the story the 10th to 12th year students are only required to take at least four core classes so they can drop the classes that they do not want to specialize in, they only need to take one of the specialized classes so they can focus on their chosen magic, and two electives. for the purposes of the RP let's get rid of the electives for now and leave it as flavor text for the RP.
With the above information in mind we can say that everyone must have five classes total, four of the seven core magic, one specialized class.and one elective,
Using that information I'll make an example using Toby.
Let's say that Toby is only taking Potions, Herbology, Defense Against the Dark arts, and Transfiguration. For the Specialized Class he's taking Voodoo, and two electives. Let's say that Eleventh year Luna's have Potions with Astra, Herbology with Solis, Defense Against the Dark Arts with Astra again, and Transfiguarion with Terra's. For Voodoo classes since it's a specialized class anyone who's interested in the subject as long as they're in the eleventh year. As for his electives since they're normally one to two year only classes anyone who meets the classification can attend the class regardless of year and house.
Using the above we can figure out that Toby has Potions with Cliodhna, Charlotte, and Thomas (but probably not Thomas?) if they're taking potions as well, Herbology with Nova and Jay if they're taking it, Defense Against the Dark arts with Cliodhna, Charlotte, and Thomas again, and then Transfiguration with no one since there are no 11th year Terra characters. In his Voodoo class he can have it with anyone as long as they're taking it as well. And as for an elective hr can have that one as well.
I've asked HOAH about all this class stuff, but he hasn't replied yet so I don't know if this helps or a total waste of time, but knowing me I'll be making a schedule of the seven core classes, and the special classes, and where the electives go.