Amen, Bro.
Now, does your character have any reason to leave cities? If so, it would be easier to run into trouble, hence making it easier to get a first kill...
If not, you may have to make up something to justify you murdering someone in-town (Which I wouldn't suggest)
Your best bet is probably a Bandit.
My character's first kill (Before he was cast out and became corrupted) was a total accident with a potion he gave someone, which they had an allergic reaction to and died, but, no one knew that, so they accused him of murder.
I've come to the conclusion that I'm gonna have to change my characters mindset before he kills for the first time, meaning I'm gonna cloud his judgment. I can see him making decisions that he normally wouldn't through the intervention of Deadra (Deadric quest,) alcohol, or Skooma. Since Skooma seems to function as an "upper," it would make sense that it could cause him to frenzy and lose control. Especially if he was on the tail end of a high, coming down, and desperately trying to find more before withdraws begin. Drug addicts going through withdraws, especially on stimulant drugs, can become very angry. Alcohol is viable for obvious reasons, we all know what can happen when someone drinks WAY too much. I'm liking the skooma idea, as my character suffered a large loss before the events of Skyrim and has motivation to 'escape from reality.' Seeing it written really makes me like the drug addict idea. He's either fiending for skooma or extremely high on it, takes something the wrong way, and it a drug induced rage, kills someone. The time he spends in prison would basically be a 'detox' period. He kills, gets off the drugs, and has time to reflect and deal with the kill however he can. Maybe lose it a little. Three birds with one stone.
I'm thinking... in Windhelm, those guys who are harassing that Dunmer when you first enter, maybe he's so out of it that he believes the men are talking to him, and feels threatened, and he so terrifyingly confused and detached from reality that he murders one of them because he thinks they're a threat. It defiantly gives him a reason to desire redemption.