Since Diablo 2 I've had a fondness for Paladins, a skilled warrior with healing skills and bane of the undead. But how to RP one i Skyrim?

He would use 1h and a shield. Probably a Silver sword or a regular steel sword. No deadric stuff of course. His armor has to look good, what kind fo heavy armor would he fit in?

The shield Spellbreaker seems good for a paladin. Would the armor be dwarven as well?

What "god" would he worship?

He would use restoration both to heal himself and others but also for turning the undead. He would never kill some one unless he has to, or unless they are undead or necromancers and so forth. He would not go on a killing spree for greed. He would be driven by the good for others.

Help me with suggestions on gear, worship, general RP style and perks.

I'm very interested in trying to RP for the first time in my life.

Well as far as the one handed weapon, Dawnbreaker is an excellent choice. Meridia is against the undead and is devoted to destroying them. Spellbreaker would definitely be a quality choice for the shield. As far as armor in general goes, if you want the gold plated look then go for dwarven. But for true RP you might not actually want it. The mind set of paladin would be that the armor is fit, protective, potentially closed in as to prevent disease/rot/unholy essence from getting to you in the midst of close quarters combat, and pure. Dwarves were twisted, diabolical crafters. The background of those who designed the armor might want to be considered. However, the Dwarven armor is closed in, bright, and intimidating.

God worship is a little more open. Where being a knight of the divines is morally good and would be looked upon as righteous, it's not necessarily a paladin. You could be a worshipper of Meridia, opposing the undead. But that would be viewed as possibly immoral, being a daedric lord. However, it's up to you decide whether you wish to be viewed as morally right or simply to be morally right according to your own beliefs. If you do choose the divines and want to be specific, I would suggest Kynareth or Stendarr. Kynareth is probably a bit more nature-esque but is also closely related to healing magic. Stendarr is obviously the god of Mercy and would fit a morally good warrior.

Also if you choose to have nothing to do with the Daedric lords (being viewed as immoral in general) Then I would suggest you take up enchanting (or rely on finding) and use a sword (preferably a mace) enchanted with Banish and/or Turn Undead. Silver weapons I tend to relate to headstrong vampire and werewolf hunters that are rather immoral and solely desire the most destructive, specialized tool for the job, but that's just me.

And, if you're on PC, I'd suggest looking into immersive armors for the proper armor. Very good lore friendly crusader armor there. There's mods for templar armor, but that's not very lore friendly.