D&D 5E - Best Fighting Style+Weapon+Feats for Paladin (Oath of Vengeance)

At level 1, take Polearm Master. (Use a Glaive or Halberd)

At level 4, take Great Weapon Master if your party can boost your chance of hitting, or +2 Strength if not.

At level 8, take +2 Strength

If you hit level 12, take Great Weapon Master if you haven't already, or +2 strength if you have and don't have 20 strength yet.

Polearm Master gives you an extra bonus action attack every round, which not only adds to your DPR but is another opportunity to use Divine Smite. It also adds to your defensive capabilities: The second ability it gives you is a free attack of opportunity whenever an enemy enters your (10-foot) reach. This combines very well with your level 7 feature Relentless Avenger, which allow you to move your speed after an attack of opportunity. When an enemy approaches you, hit them with your polearm, then use the free movement to get out of the reach of the rest of their movement.

Great Weapon Master allows you to take -5 to hit for +10 to damage, which works extremely well with the advantage granted by oath of enmity, but it's outperformed by +2 Strength in the case that you're not attacking at advantage (so, every time except the once/day when you've used your vow). If you have some other way of getting advantage (Variant Flanking rules, a Wolf Totem Barbarian, etc.), or other ways of boosting your chance to hit (A cleric who's always casting bless on you), then Great Weapon Master is better.

Great Weapon Fighting is the best fighting style you can use if the DM is ignoring sage advice and letting you apply it to Divine Smite.

The main advantage of Half-elf is access to the phenomenal Elven Accuracy feat, which gives you +1 to Dex or Cha and a third D20 roll when attacking with advantage, but it doesn't work when attacking with Strength. You could use a Cha-focused build and use the Hexblade feature to have Cha as your attacking stat, but setting you back 3 levels is too high a cost if you're only going to level 10. Otherwise, Variant human is better in a feat-centric build like this, having an extra feat puts your ASI progression ahead four levels on a build that needs every ASI it can get.

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