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.