MM7 Races have a minor impact during gameplay where certain foes will prioritize characters of a certain Race. A few items are only usable by a certain Race.
The primary impact of Race is during character creation as starting statistic values are determined by Race and more importantly the Cost in Bonus Points to raise a given statistic and Max Value is also impacted by Race. Note that boosting statistics during gameplay is NOT impacted by Race.
Human details
Humans can be universally effective in any Class. Humans will typically be targeted by Elven foes. Humans have exclusive access to the Mind's Eye helmet which boasts these qualities: AC+10, INT+15, PER+15, Regen SP.
Base Value Cost to Raise
MGT 11 1x (Max 25)
INT 11 1x (Max 25)
PER 11 1x (Max 25)
END 11 1x (Max 25)
ACY 11 1x (Max 25)
SPD 11 1x (Max 25)
LCK 11 1x (Max 25)
Elf details
Elves are most effective as a Sorcerer but can also work well as a Druid focused on spell casting. Elves will typically be targeted by Human melee foes. Elves have exclusive access to Elven Chainmail which is a specific item that boasts these qualities: AC+30, SPD+15, ACY+15, Regen HP -- however, this item cannot be worn by Sorcerers or Druids.
Base Value Cost to Raise
MGT 7 2x (Max 15)
INT 14 .5x (Max 30)
PER 11 1x (Max 25)
END 7 2x (Max 15)
ACY 14 .5x (Max 30)
SPD 11 1x (Max 25)
LCK 9 1x (Max 25)
Dwarf details
Dwarves are most effective as a Paladin or Cleric. Dwarves can go Knight or Ranger as well but the low SPD/ACY will hamper their melee damage output. Dwarves will typically be targeted by Goblin and Troll foes. Dwarves have exclusive access to the Forge Gauntlets which boasts these qualities: AC+10, MGT+15, END+15, Fire Resist+30.
Base Value Cost to Raise
MGT 14 .5x (Max 30)
INT 11 1x (Max 25)
PER 11 1x (Max 25)
END 14 .5x (Max 30)
ACY 7 2x (Max 15)
SPD 7 2x (Max 15)
LCK 9 1x (Max 25)
Goblin details
Goblins are the best choice for ALL Classes other than Sorcerer and hybrid classes intent on only spell casting. Goblins will typically be targeted by Dwarven foes. Goblins have exclusive access to the Elfbane 2h-Sword which boasts these qualities: 3d4+12 DMG, 2x DMG vs Elves, .5x DMG from Projectiles.
Base Value Cost to Raise
MGT 14 .5x (Max 30)
INT 7 2x (Max 15)
PER 7 1x (Max 25)
END 11 1x (Max 25)
ACY 11 1x (Max 25)
SPD 14 .5x (Max 30)
LCK 9 1x (Max 25)
Attribution
Official manual has this info here.