What race would be best?
What armour?
What skills should I use?
Race wouldn't really matter, but if you're going for a Medieval style character, then probably Breton.
Join the Dawnguard and use both their Heavy Armour and their Sunlight Spells. Heavy Armour, 1 handed, Archery, Light Armour (helps to be versatile), Restoration, Destruction, Smithing, Enchanting, Speech.
And if you don't have Dawnguard, then Steel Plate armour would probably work, too.
-=Race=-
If it really matters, Breton or Imperial fit the typical Paladin mold.
A Breton character could be part of http://uesp.net/wiki/Daggerfall:Temples#Templar_Orders
An Imperial character could be trying to bring back the Knights of the Nine.
-=Armor=-
Steel, Steel Plate, Blades(?), possibly a robe on the body like the Vigilants have.
-=Skills=-
Defo Restoration. Dawnguard light spells will be useful as well as Turn Undead spells. Heavy armor and one handed, too. Maybe smithing and two handed?
I had a Redguard Paladin once who used Dwarven Armour for the aesthetics, without the helm of course.
He used Dawnbreaker in his right hand, and a powerful healing spell in his left. Spellbreaker is also an excellent choice!
There's lot of fun Restoration spells that will also let you scare away undead.
I did make a Crusader build some time ago, based on the closest class to a Paladin that has been in previous TES games. Maybe you'll find it useful
http://theskyrimblog.ning.com/group/character-building/forum/topics/character-build-the-crusader-4?xg_source=activity
Being a paladin is tough,because you have to master magic and physical perfection. You also have to devote yourself to some kind of cause, like a god,or killing vampire/evil, or even a daedric prince. I've started a build like that and so far I've gone with,
Breton
Heavy armor - Dawnguard armor,or dwarven, or when I get high enough,dragonbone.
Restoration
Destruction
One handed
Smithing
Enchantment
Also,do the meridia's beacon quest for an epic paladin sword.
I just got done playing a war priest, which is basically a fancy name for Paladin.
One handed (maces)
Heavy armor
Restoration (all spells)
Smithing
Alteration (just for the magic absorbtion)
Thats basically it. Very noble, does good, helps others. I will add that I added conjuration BUT only for the banish daedra spell as I can totally see a paladin type character using that. I will also add that I did by no means actually use conjuration (raising dead, atronachs). I strictly paid for my training to get my level high enough so I can get the spell.
Race doesnt matter. I stuck with Nord. Any heavy armor would work as long as it doesn't have an evil appearance. MAces are considered a holy weapon so theres your weapon. Amulet of MAra and bond of matrimony for the added restoration cost reduction. Adept college hood for added magika.
And as far as skill points I think I did a ratio of 5-1, favoring magika over health.
Race: Imperial is perfect or Breton/Redguard.
Armor & Skills:
Heavy Armor (Steel plate, Dwarven or other)
1H (sword or mace)
Block (for shield)
Restoration
Smithing or Enchanting (optional, one or both depending if you need them on a high difficulty setting)
Redguard
Heavy Armour (Dwarven is preferable until Ebony at higher levels)
Restoration, Heavy Armour, One Handed and Archery. Alchemy fits in nicely as well, especially for Vampire hunters.
Really? It's a common character type that usually involves heavy armor, sword n board mixed with a splash of magic and faith...pick your favorite equipment/spells from those staples
Both are improved with the same smithing perk so try them both out and see which one you like best.
And that ebony mace looks rocking,the best looking mace in the game.
My Templar build used Dawnguard Heavy, Dawnbreaker, and Spellbreaker / Restoration. I also did a "Dark Templar" who used Ebony armor, an Ebony Mace, and shock magic.
Oh yeah, full set of ebony armor with an adept hood, weilding an ebony mace looks dope.
Take a look at http://theskyrimblog.ning.com/group/character-building/forum/topics/character-build-the-paladin It's a somewhat long read, but I think it'll fit quite nicely.
Personally I'd use steel plate, just because I think it looks cooler.