How should I build a “paladin” character

If you're going for a tank build (stand there, violently attacking and taking tons of damage) go heavy. This would be melee > magic.

If you're going for a kiting build (run around, fire off spells, then run in and attack) go light armour OR (IMHO a better option from what I've seen; the stat boosts are huge) enchanted robes of something. This would be for a magic > melee build.

And if you're looking for bonuses, I believe they are equal. If not, just enchant your own.

This is pretty much the same build that I've been using. I put a bit over half my total points into Magicka, most of the rest into Health, and very few into Stamina. I don't use many power attacks, and when I do, it's to finish the enemies off or stall for time while my Magicka is regenerating. It's working for me so far.

You will get enough perks to fill up 4 perk trees with room to spare, so don't worry about starting into another. I'm focusing on Conjuration, Destruction, Restoration, and One-handed, with a minor amount in Light Armor. Putting a point or two in a tree just to get a slight bonus isn't going to harm your chances of completing other trees.

Even if you completely focus on Conjuration, chances are you won't use every perk in that tree. You might focus on Atronachs over reanimating corpses, or you might not use bound weapons.

Just pick whatever perks you want and don't worry about it too much.