Serial killers are often mentally imbalanced. From their perspective, what they are doing might seem perfectly justified to them. So if you do something like that from their perspective, they might constantly make justification for their actions, erratic dialogue, and things that might appear insane from our perspective. I've never written a serial killer before, but this is a small piece of what I might do.
I like it when I can relate to them, and sympathize with them, but at the same time be completely appalled by them. They have to be believable, and they have to have some motive, even if it relies completely on their own messed up logic.
An understanding of how mental disorders and sociopathy actually manifest.
If you're going to write this kind of story, I would suggest doing a lot of research before you even begin writing. A particularly good author is Robert Ressler. The guy is basically responsible for modern criminal profiling and has a great insight into how sociopaths develop, think and perceive the world.
But there's mountains of books out there on criminal psychology, offender profiling, general behavioural science and psychopathology of all kinds. It's a fascinating topic and can only benefit your writing. Mind you, if you don't have the heart for reading it, you may want to reconsider. It is as frightening as it is fascinating.
You expect others to share their ideas but tell us nothing about yours? It is hard to tell how your story would work best when we don't know anything about your plot and character.
In any case I'd suggest that you read stories and novels in that genre. Anything about murderers. Make sure you know a few things about forensics and psychology, too. Not to copy, of course, but to see how other authors deal with certain issues and how things work. Then find out what works best for you.
The problem with your original post isn't a typo: it's a total lack of punctuation. If you at least separated things out into different sentences, it would make it much easier for people to understand what you're saying.
I gather that people don't tend to put much effort into forum posts as they do with actual literature, but it seems a little silly for a writer to drop punctuation altogether. You'll need to use it for your serial killer story, so you might as well get some practice in.
If you're doing it as the killer is alive, I'd suggest you tell it from the perspective of what he sees in his head.
Assuming this guy is crazy... you could call the screaming "singing," make tracking his/her victims seem like a game in his POV, antagonize the authority as austere and parental. Hallucinations, under-the breath whisperings, violent impulse thoughts to build tension. Stuff like that.
If not, then read "Watchmen" and see if you can take a leaf out of Rorschach's book. He could've been a serial killer.
I am working an a story about an spree killer, a real case. I tried using the perspective of the killer himself, but it limits the story pretty much. Mine ends up executed, so unless I put him telling the story from the grave I can not get it work properly.
A good option is to divide the novel in parts and use the main character (the killer), as well as other characters around him or her to tell the story, relatives, old friends, psychiatrists. A man telling his own story works in movies, where you have flashbacks, is more visual. In a book, it can work, but you loose part of the character in it. It seems flat from my point of view.
Ugh... I do not know if I explained myself or nor.
In any story with a strong, immediate POV character, it's most effective when the reader can submerge himself in the POV's viewpoint. When this is successfully done with a deeply unsympathetic or evil character, it can be extraordinarily disturbing.
I'd do a lot of research into psychological profiles of real serial killers so as to understand how they think and be able to represent it in a way that's true to life.
I'm going to guess that you mean you're going to write a story about a serial killer through the perspective of the serial killer. I know if I were to read that kind of story, I'd be interested in the psychological aspect. Or rather, how the serial killer thinks. What makes him (or her!) want to kill others? What's his/her motivations to kill? Why do they think murder justifies their actions? Stuff like that.