paladin strength build how to do it? or should I just go with dex?

[Pex]

It would help to ask your DM if he would allow Great Weapon Style's effect to work on smite damage. By the book it does, but Sage Advice says no. If yes, there's your build. You wouldn't need Great Weapon Master feat. You will do plenty of damage. Doesn't hurt to have the feat, but you aren't in need of it for the damage. The game does not become unplayable if yes. It is the feature of allowing it that the paladin would dish out a great deal of damage in spike pattern. He already has the spike pattern with smites in general. This increases the peak. A fight against something you'd smite anyway ends one or two rounds earlier than without it. It's the paladin's turn in the spotlight.

If no, you're back to where you started. I'd recommend go for the stereotype. Take Dueling Style for the +2 damage. It is significant over the rounds. Use a shield and heavy armor for your AC. Initiative is good to have but not that important.

Your weakness is in range. You have none. If you were to go DX build you could do something with bows, but then you're not using a shield and still can't Smite. You could lump it and let other party members deal with range attacks. When you need to close in on the enemy but can't reach them yet, that's a good time to buff yourself with a spell or Channel Divinity. If reaching the enemy is not possible, this is where other members of the party get their turn in the spotlight. For these occasions you casting Bless while the cleric does something else might be the thing to do. If your lack of range is hurting the party due to your limited or no actions, consider Magic Initiate feat and pick up a couple of Cantrips. Variant Human gets that out of the way at character creation to focus on other things as you level.