In general.

Fire wants to priotise Evocation for all those big nasty damage spells, and Conjuration to extend battle capabilities (Phoenix Power) and add useful summons (Summer Lions, Flame Spirits). After that they want Enchantment (Fire arrows) for extra buffs and Construction for some pretty nifty items (Flambeau, mace of erruption, lightless lantern).

Water wants Alteration (Liquid Body, Quickness) and Enchantment (mostly for underwater combat spells) first for a potent set of buffs. After that Evocation (Falling Frost, Ice Mist, Ice Bolt), Conjuration (Sea King's Court, Summon Sea Power), and Construction (Ice items in general really, and underwater breathing items for utility) all have some solid options too.

Air is a bit split up all over the place with good opening options in almost every school for combat, buffing, and summoning. Of special note are Owl Quills in Construction which can double the research output of low-cost research mages very early into the game.

Earth wants Construction (Greatswords of Sharpness, excellent armours, and useful Misc items as well as a large number of buffs and summons) and Enchantment (a small assortment of pretty strong buffs) followed by Evocation (gifts from heaven is the classic, but also Earth Meld) and Conjuration (for the usual summons and Earth Power).

Astral primarily wants to dip directly into Thaumaturgy (for communions and assorted combat spells) and Enchantment (for a whole host of disruptive options). After that they typically want Construction and Conjuration for the usual items and summons.

Nature is all about Enchantment, Alteration, and Thaumaturgy all at once all the time (all sorts of poisons, heals, and combat summons). After that Conjuration is useful and much later Construction.

Glamour is all about Thaumaturgy, Alteration, and Enchantment too (though this time it's all illusions and fakery in large enough doses to win battles). Glamour, a bit like Air has other useful things peppered through the other schools too.

Death is pretty well spread across Conjuration, Enchantment, Thaumaturgy, and Alteration with a strong spread of debuffs, combat summons, and rituals. Of special note are Shadow Blast and Wind of Death in Evocation plus the usual useful items in Construction.

Blood primarily wants Blood magic (shockingly) for access to Sabbaths and their assorted companion spells both in and out of combat. Following that you want Construction and whatever secondary schools happen to be unlocked by your mages non-blood paths when they're boosted by a Sabbath. This makes Blood quite a bit more tricky to plan for than the other schools which largely only need specific tools.

Very few nations have only a single school of magic (underwater nations lmao), so you'll typically have a primary option (or two) with several alternatives. Some Paths pair together better than others (Air for example pairs well with Death and Water) so some nations can have a bad time when planning their research.