What type of character has been your favorite so far, and why? What difficulty? What gear? What do you like about it?

Mage so far, but im about to try out a Nord who shield charges everywhere and uses his fists, heavy armour perk and enhanced gauntlets with fortify unarmed. He will fight for the Empire.

Mage archer with auriel's bow and destruction magic

and a woodcutter's axe as a backup weapon

Just a pure and simple Mage for me. I've had a number of them.
Another interesting build is a Battlemage, who exclusively uses bound weapons. The weapons drain your magicka quite a bit, so you'll have limited spell casting abilities in the early levels ... But the heavy armor balances that out for you

A Hobo type character who isn't allowed to have good weapons, is only allowed to wield an iron knife that stays un-upgraded. He also uses a wooden bow to hunt meat with. (usually rabbits or small game like foxes.) Also he levels up so that enemies will get stronger but I put all points into Magic which he isn't allowed to use anyways. Any health regains must come from scavenged potions.

My Wood Elf.
He fought for the Empire
Rose to the leadership of the Dark Brotherhood
Restored the Thieves Guild
Saved the College of Winterhold
Is Harbinger of the Companions
Murdered Alduin and Parthuurnax
Knows every skill. He is maxed out completely.
Married.
And currently hunts vampires

One-Handed, Block, Light Armor. Get good with the shield or get turned into paste.

I am playing a really creepy Necromancer. Been really embracing Necromancy and Bound Weapons, along with Namira's "gift". It is making for a truly fun RP experience, and keeps combat fresh by relying on dead bodies. If I see a pile of dead bodies, I go crazy and use The Ritual Stone. So much fun