I think different races should get different kinds of magic, and almost all should have disadvantages.
Humans could have typical RPG style clerical/religious magic.
If any of you have read
the black magican series from Trudi Canavan, the human healing magic should be like healing magic in there.
There, healing can almost instantly close any wound, or fix broken bones, but the magican has to touch the body, and the magic can't fix what the body could not heal itself. Also, unlike healing in typical RPG settings, healing magic weakens the guy who is being healed, because he uses his bodies own reserves and nutrients. So its more like natural healing getting extremely accelerated.
(Something like that could be made by a temporatry and significant stats decrease after being healed, worse wound = bigger decrease)
Also priests can bless warriors, which would be like a very minor version of a martial trance and maybe makes human warriors unable to retreat.
Elves have typical natural/druid magic. Animate tree, enrage war animal, maybe even turn your animals around. Maybe a way to bless wood so it becomes like iron in its properties.
Dwarves... I like the Warhammer approach. "Magic is for robe wearing wussies, we use runes". Job would be runesmith, and very hard to train (or even a noble maybe? Attracted by a alchemy lab and several successful alchemists living in your fort?). Runes are engraved into a weapon or armor, and then filled with metal dust, where more valuable dust wields better effects.
This is a *steel breatplate* by Urist McLegendaryArmorer.
It is engraved with +runes of hardening+, imbued with silver dust by Urist McRunesmith.
Besides that he might be able to set "traps" inside rocky corridors and rooms, that set the first enemy on fire, or makes them panic, or sleepy, or something else.
Dust is produces by alchemists, who also use it for potions. Potions are used by soldiers, who have to carry them instead of waterskins/flasks (or inside them), and they raise a stat, depending on the skill of the alchemist and the metal used for the dust.
Goblins... something that includes lots of blood, abducted babies and more blood.
EDIT: Fixed the broken formating, wrote it at work on an outdated IE