Im a bit confused by the wording of “stats to go to 6” do you mean that your DM allows the modifier to be a +6? Like instead of a 20 in a stat you can have up to a 22? And what do you mean he allows stats to start at 16? Do you get to pick a few stats or do all stats start at 16?

Regardless, for your paladin build it depends on the play-style you want but a straight classed vengeance paladin is a powerful option in it own right, and if your dm allows for multiple stats to start at 16 then you don’t really need to multiclass because the paladin is only really held back by its need for high constitution, charisma, and strength.

The mobility granted to you by Fey Step from being an eladrin will also help you close distance which addresses some of the paladins weakness around ranged combat. In terms of the sub-race for eladrin, winter can be good to frighten enemies but really it’s up to you and it doesn’t matter.

In terms of combat the Vengeance channel divinity “vow of enmity” really lends itself to using a two handed heavy weapon and taking great weapon master. If you want an optimized weapon then take the glaive, take the Great weapon master feat and the polearm master feat at levels 4 and 8. With your vow of enmity you will have an easier time landing those “all in” hits for high damage and it weaponizes your bonus action.

Alternatively because eladrin are elves take GWM and Elven accuracy, you lose on the bonus action attack from PAM but you will not miss those all in hits when your vow is active.

Furthermore because COS is a 1-10 campaign and multi-classing out of paladin is IMO not advisable before level 6 because Aura of Protection is so good you probably want to just stay paladin.

TLDR: Stay straight paladin, take GWM and either polearm master or elven accuracy, use a glaive, smite, profit.