You're in a very nice position as an actor when you're portraying a piece of history that actually happened and portraying characters that actually existed. There's so much more to draw on and your research as an actor becomes much easier than if it's some fiction that you're trying to create a world around and background and history.
I think you've really got to cling to what makes sense to you. Obviously, I'm not a serial murderer in my real life, so that's where you have to delve into and do all the research. But, you have to find something likable in the character.
It's funny when you know you're playing two characters and you're aware of how you have to play each one into your performance of the other. You're constantly at the back of your mind thinking and it all gets a bit confusing.