DnD classes will fall into 1 of 2 categories when it comes to stats - SAD and MAD. These stand for Single- or Multiple-Attribute-Dependant - and the Paladin is very much MAD. For SAD characters, you throw everything into getting that primary attribute to max out, and the rest is just gravy. A MAD character will focus differently. It’s better to have multiple mid-high stats than maxing out a single stat.

As a melee character, you’ll need high Strength and Constitution, and as a paladin, a decent Cha. Getting these all to mid-high will mean you neglect your Dex, Int and Wis.

Most people play with significantly higher stats than the standard array, which the monsters are balanced for, but since I don’t know what stat arrays or generation method you will be using, we’ll look at the standard array. 15, 14, 13, 12, 10, 8

Realistically, you’ll want CON as your highest stat. Staying power will be more important than pure DPS as you are the tank and healer. Smite will help with your damage output.

That being said, you still need to be able to hit things. 14 goes to Str.
Cha will be prioritized next, as this directly affects your spell saves, how frequently you can use some class abilities, and later on how strong the saving throws of you and your party are. 13 here.

Generally, I’ll prefer WIS > DEX > INT here, but you can adjust it based on what saves you think will be targeted most. WIS tends to be the save targeted by mind control most often, Dex for AOEs, and INT is super rare, but also very deadly. There are arguments to be made for each one to be prioritized. Pick your poison.

For Races,
Aasimar is pretty strong. Volos versions will have +2 Cha and either +1 Con, Wis or Str. MotM Aasimar is even stronger, with a “you choose” spread of +2/+1 or +1/+1/+1 and all of them have a good doubling up of free healing if you want to ensure that your party never stays down.
Bugbears are also a strong choice. +2 Str and 10ft reach are pretty compelling options.
Dragonborn have good stat distribution too - +2 Str, +1 Cha. These pair nicely with Paladins, and the energy resistance is really nice. However don’t put too much stock in the breath weapon. It’s low damage, and 1/short rest.
Volo’s Goliath is a strong choice if you want to lean into the tank options. +2 Str, +1 Con, and proficiency times / long rest, you can reaction to reduce incoming damage from an attack by 1d12+CON.

Finally, you can’t discount Variant Human or Custom Lineage for the free feat. These things can pack so much power into you that it’s worth the loss of stats. War Caster will let you tank up with a shield from day 1 without it impacting your spell casting, and give you advantage on Concentration checks which you will probably be making a lot of. Paladins don’t get a lot of offensive spell options, but have good concentration-based buffs. Resilient Con for +1 con and proficiency bonus to Con saves is really strong.

If you want to lean into pure high damage numbers, the bonus feat is the way to go. Variant Human Paladin of Vengence, pick up Pole-Arm Mastery and use a glaive or halberd. As soon as you can, grab Great Weapon Master. At level 5, you get your boss-killing option in Vow of Enmity, which gives you advantage on all attacks against something for 10 rounds, with 2-3 attacks per round (2 on the round you activate it, 3 every other round). A Glaive attack would be either +5, 1d10+2 when you don’t expect to hit easily, or +0 1d10+12 when you have advantage or when you do. The math has been run, and it’s essentially always worth it, in a damage per round calculation, to do this when you have advantage, and if you crit it goes Nova.
2d10+12+6d8 (lvl2 smite) = 49 average damage, 72 damage max. Higher if you have a magic weapon, or better stat spread.
And you still get your Heavy Armor AC of 17 or 18.

you can easily get higher numbers with multi-classing shenanigans, but these are almost always 1 trick ponies, and often once a day things. A solid paladin can keep trucking for much longer, and if you have any support-oriented party members who will buff you (Haste, Bless, etc), then you’ll be a juggernaut.