FirbolgVGtM: Apart from the strength increase, this race doesn’t offer much for Fighter.
Air: The Dexterity boost is good for a ranged build, and limited flight helps you make it to a sniper’s perch at lower levels than flight would normally be available to you.
Earth: Strength, Constitution, and the ability to ignore difficult terrain. An excellent choice.
Fire: Intelligence, a cantrip, and a spell make this a great lead-in to an Eldritch Knight.
Water: Wisdom doesn’t do much for a Fighter, and the resistance to acid is situational at best.
GithMToF: The two Gith races are polar opposite in terms of their usefulness for a Fighter.
Githyanki: Intelligence, Strength, and bonus spells make this a great lead in for the Eldritch Knight.
Githzerai: Nothing useful for Fighters with this race.
Gnome: Gnomes don’t make particularly good fighters. All their racial abilities are geared towards Wisdom and Charisma, which aren’t important stats for a Fighter.
Deep (Svirfneblin)EEPC/SCAG: Forest Gnomes are typically a better choice here.
Forest: These Gnomes make good Dexterity-based Eldritch Knights.
Rock: This race offers very little to the Fighter.
GoblinVGtM: Dexterity, Nimble Escape, and Fury of the Small add a lot to a melee fighter build.
GoliathVGtM/EEPC: This race was made to be a Fighter. Strength, Constitution, free Athletics proficiency, and Stone’s Endurance all lend themselves to a powerful Fighter.
Half-Elf: Choosing which stats to increase allow you to prioritize the correct build for whatever flavor you’re going for. The subraces add helpful abilities as well but are generally outshone by full-elves or humans.
Standard: This race gives you all the skills you need to be the face of the party, or to fill out the class skill list.
AquaticSACG: Only useful in an aquatic campaign.
DrowSCAG: The bonus spells are nice, but otherwise this race doesn’t offer much.
Moon/SunSCAG: Losing a skill for a cantrip is situationally worth it. And the weapon proficiencies are redundant considering you’re proficient with all the weapons already.
WoodSCAG: The bonus speed helps, but otherwise this race doesn’t offer much.
Half-Orc: Strength, Relentless Endurance, and Savage Attack make you a dangerous berserker, especially combined with the Champion’s increased critical hit range.
Halfling: Dexterity increase makes for a good finesse-weapon or Dexterity-based Fighter. The Lucky ability also lends itself to Fighter’s spread of attacks.
Lightfoot: Not a good choice for a Fighter.
GhostwiseSCAG: Not a good choice for a Fighter.
Stout: Dexterity, Constitution, and resistance to poison make this a strong choice for a Dexterity-based Fighter build.
HobgoblinVGtM: Saving Face will give you a second chance to hit with a missed attack. The Constitution and Intelligence lend itself to Eldritch Knight.