Right now I'm thinking of making a Dark Elf Paladin because I love Dark Elves. Thing is that I want to use Daedric Armor but that doesn't seem like what a Paladin would wear, I also want to use Daedric weapons specifically a Daedric Longsword but that also doesn't seem very much like a Paladin.
What class do you guys think I should play?

Maybe go light armor instead? Glass Armor is very paladin-ish*.

What class do we think you should play?
You mean like a class that allows the weapons you want to use?
Or what weapons to use for a paladin?

Dwarven looks good for a pally and both dawn and spell breaker work nice too, but if your looking to use daedric equipment you could rp some sort of nercromage dark paladin.

Can you explain to me what does the class do and how they behave?

sounds like you want to be a death knight. Feel free to toss in some destruction magic based on your choice of a dark elf.

Do heavy armour.

Primary:
One handed mace/sword
Alteration (Flesh spells before battle)
Restoration (During battle)
Heavy Armour (Steel and Ebony for Pure Pallys, Dwarven and Daedric for Death Pallys)

Secondary:
Speech
Lockpicking
Enchanting
Alchemy
Smithing up to level 60
(Use potions and enchanted items to boost your smithing levels up to temper items you have received, get arcane tempering perk)

It sounds to me like you aren't sure what you want in your character. A paladin is generally a holy knight who uses light and healing; quite opposite of what Daedric armor would represent. Why would you then want Daedric armor? Or if it's the Daedric armor you really want, why do you want to be a paladin?

for a Paladin use:

- Dawn Breaker (1-handed sword)
- Spell Breaker (Shield)
- Steel plate armor or Dwarven maybe even Ebony armor. (they all look knightly)
-Restoration (Holy magic for healz)

Two things. One, for ES lore it is possible what you are really wanting to play is a Crusader, and as I recall tons of high level Crusaders in Morrowind wore Daedric armor, and Crusaders would not have a problem using it. Really I don't think a 'Paladin' in our sense of the word would either. Daedric Armor is simply the best armor available just like heavy steel and plate is in previous games or stories you hear about Paladins. It is made from inanimate objects you get from fallen enemies or left overs from the Oblivion crisis. There is no reason to assume that is from flayed flesh of dremora as it was in Oblivion, and if so why not use it anyway. Do you cry when you knock a Dremora into a pool of lava? No.

Your task young sir is to defend the realm from all foes and you will need the best protection you can get. Any less would be a diservice to those you serve.

This

Plus alteration (protection spell is a bit part of like pally will do)

Speech for persuade

And pick one crafting (personally I prefer alchemy over enchant/smith)

My Paladin of Akatosh, Ahlanna Brightblade wields Dawnbreaker and wears her enchanted, legendary Blades Armor called Akatosh's Sentinel. Its very cool.