Here's a couple of guys to start you off:
Nord Hunter
Race: Nord.
Alignment: Chaotic good.
Perk trees: archery, two-handed (swords), block, speechcraft (from trading meat and hides).
Companion: dog.
Quirkiness: only wears furs.
Gameplay: relies on his faithful dog to keep monsters distracted, but if any get through, he can swing a mighty sword like few others. As he improves his archery, he will kite more and rely less on his sword, to avoid getting demolished in melee due to his lack of armor.
Story: after the harrowing ordeal in the intro, he decides to abandon his neutral, nomadic life, join the Stormcloaks, and help rid Skyrim of all its enemies.
Jester
Race: Argonian.
Alignment: Chaotic neutral.
Perk trees: destruction, illusion, sneak, pickpocket.
Companion: none.
Quirkiness: known to cast Frenzy in inns and other public places for his own amusemant.
Gameplay: sneaky spellslinger. In the early game, relies on illusion spells to keep monsters off his back. Once he gets quiet casting, nothing will stand in his way.
Story: this mad lizard's shenanigans and penchant for larceny got him in trouble with the wrong crowd. He fled to the most remote region of Tamriel possible, but was captured soon after crossing the border into Skyrim. Those who mistake him for a fool capable only of cheap parlor tricks will quickly learn their mistake, before being turned to cinders.