For Paladin VGTM has
Aasimar: +2 Charisma, Darkvision, Necro/Radiant Resistance, Healing Hands (heal level damage with a touch once a day, touch action), Lightbringer (light cantrip), celestial language, at 3rd level a subrace power that transforms you, boosting damage and some other effect, +1 attribute based on subrace.
The race itself is basically being a Paladin, and its all goes well with the Paladin class, reinforcing the Paladins themes.
Firbolg: +1 strength, +2 Wisdom. Firbolg magic (cast either detect magic or disguise self once per short rest), hidden step (1 turn invisiblity once per short rest), leaf and beast speech (can talk to animals and plants), Powerful Build, speaks Elvish and Giant. Strength bonus is nice. You can share Detect Magic and Disguise Self with your mount. Powerful Build and high strength is go for moving and lifting stuff, congrats on beingbthe parties mule.
Goliaths: Same as before
Lizardfolk: +2 Con, +1 Wisdom. Swim Speed 30', hold beath 15 minutes, can build primative weapons and shields using dead bodies during a short rest, natural armour, bite attack, natural weapon and unarmed attack, can do a special bite attack as a bonus action that grants temp hp for eating your target language Draconic. Can one use smite with a bite attack?
Kenku, +2 Dex, +1 Wisdom, advantage on crafting rolls to copy something, choice two roguish skills from a list of four, mimicry. Can read and write and understand Common and Auran, but not speak it. No reason it chose it, the class is straight up skill money.
Kobold- Darkvision, a once a short rest ability to great advantage to your allies as an action, pack tactics (this ability rocks), -2 strength, +2 Dex, Draconic Language. At first glance it sucks, -2 strength. In practice pack tactics makes up for that. Great for a Dexaldin, but even for a strength build, its possible to get 20 strength by high levels, with Pack Tactics, your going to be extremely accurate. Small Size is to your advantage, go with a Mastiff Mount and use a lance and shield, its medium so it can go anywhere and it will allow you to use pack tactics basically at will. Reward for most counter intuitively awesome Paladin Race.
Hobgoblin +2 Con, +1 Wisdom, +1 for every ally that witnesses your screw up on one roll every short rest, 2 martial weapon profs and light armour prof, Darkvision, Goblin Language. Hobgoblin is like a multiclass into fighter. That con is useful, but the weapon/armour profs are a waste, but its other ability is still good. Okay choice, but uninspired.
Goblin: +2 dex, +1 con, nimble escape, furry of the small, darkvision, goblin language. A Paladin with a Talent for striking from Shadows.
Bugbear: +2 Strength, +1 Dex, Surpise attack (2D6 damage), long limbs +5 reach on attack action, sneaky (stealth prof), darkvision, goblin language. One of the Best races for Paladin, if you get good at Surprising enemies. Incredible reach.
Tritons: +1 strength, +1 Con, and +1 Charisma, Triton magic which is Fog Cloud, Gust of Wind, and Water Wall once per day, the ability to take to any creature that can breath water, cold resistance and depth pressure immunity. Can breath both air and water, swim speed of 30', and speaks Primordial. If your DM will allow, I'd suggest an mount that can breath both air and water if the DM allows it. Great stats for a Paladin.
Tabaxi: +2 Dex, +1 Charisma, can double speed for a turn, but can use it again, until you use zero movement for a turn, has claws which count as natural weapons and unarmed attacks, and gives you a climb speed of 20', stealth and Perception prof, Darkvision, knows common & one language of your choice. +1 Charisma is nice, but does Smite work with natural weapons?
Orc: +2 Stength, +1 Con, -2 Intelligence, Powerful Build, Aggressive (as a bonus action you can move towards an enemy), menacing (intimadation prof), Darkvision, Orc Language. Avenger Paladin, hands down.
Yuan Ti Pureblood: +2 Charisma, +1 Intelligence. Poison Cantrip, At will Animal Friendship (snakes only), at 3rd level Suggestion once a day, poison immunity, Darkvision, Magic Resistance, Abyssal and Draconic languages. +2 Charisma is useful. Basically a Paladin with a more spellcaster focus. An Pureblood Paladin of the Ancients Oath is bane of mages, magic resistance in spades, Poison and Disease Immunity, ect...,