Let's talk about magic and spells.
Being a fan of the four classical elements, I am very much in favor of keeping Water, Earth, Fire, and Air as the schools of magic. But to avoid any of the schools being inherently superior / inferior to others, each can be assigned its specific role.
What is magic usually used for on the battlefield? Well, virtually anything, but as long as we're fitting stuff into boxes, let's split them into Offensive and Defensive spells. On the other hand, by the nature of the spells, they can be used to strengthen friendly units or weaken enemies. Both of those can be used offensively and defensively, so I think it's fair to say we got ourselves a new axis, Buffs / Debuffs.
In general, an offensive spell lets you deal more damage, and defensive one will let you avoid or revert damage. So an example of an offensive debuff would be something that lowers the defense of an enemy stack, and an offensive buff would be something that increases speed of your units, allowing them to get closer to the ranged enemy units. You can see where I'm going with this.
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So if we want to assign each school something it would focus on, we can borrow a bit from our good friend Aristotle and divide them like so. I think it's fair to say that Air with its speed and lightnings and Fire with its... well, fire plant themselves firmly on the Offensive end of the spectrum, which leaves slow and sturdy Earth and gentle Water on the Defense. Power of healing in Water and, once again, speed of Air put them closer to the Buffs than Debuffs, and the abilities of Earth to slow enemies down and raise walls and Fire to hurt them (not necessarily in the damaging sense) edge them towards Debuffs. Notice though that the focus of a particular school doesn't mean it can't do other things; for instance, Earth magic buffing defense, or Water spells inflicting cold damage.
There are also certain spells that, I think, shouldn't be tied to any particular school, as they utilize "pure" form of magic. Things like Magic Arrow or Dispel Magic can have their own little category.
Another thing that I think is worth talking about is Mass spells. Any HoMM III player knows that Mass Haste and Mass Slow are among the most valuable spells in your spellbook, simply because they consume tiny number of spell points, but produce great results. In HoMM II, on the other hand, Mass versions of the spells had to be learned separately from their basic counterparts. I think, those two solutions can be combined. A hero with high enough X Magic skill and Wisdom (speaking in HoMM III terms) that knows basic version of a spell will find a Mass version in his spellbook as a higher-level alternative. So he can cast a basic version for few mana points, or Mass version for many more.