Many criminologists think there are a few different "styles" of killer. Here's a few I found pretty quickly when trying to refresh my memory on this:
Visionary- Generally someone with major breaks from reality that make them either feel they aren't responsible or have a duty from some other power to kill. David Berkowitz, who thought the devil was commanding him to kill, was this type. Norman Bates is a pop culture example that probably fits here.
Mission-oriented- Someone who wants to better the world by getting rid of certain institutions or people. That Dorner guy who was in the news recently might qualify, or maybe the Unabomber. Manson family is kinda a blend of this and the first type. The killer from Seven might be a pop-culture take.
Hedonistic- this has three subcategories but is probably most common:
1. Lust- A lot of rapist/killers are this, but some probably fit into another category or mix with another category. Probably they are otherwise sexually unfulfilled and simply can't control their desires.
2. Thrill- Pretty self-explanatory. Killing is fun like skydiving or the way a hunter likes hunting. Someone like Charles Starkweather obvious applies, but more "traditional" serial killers have listed this a major motive.
3. Comfort- Basically killing for money or some other kind of tangible profit. Hitmen or black widows or things like that.
Power/Control- This is where most other rapist killers come in, but the sex would more be a way of showing control than about getting off. It'd be a safe bet that torturers who don't necessarily sexually abuse their victims might fit here. A lot of folks think Ted Bundy, who was considered pretty attractive and had a string of girlfriends and probably a decent sex life outside of his killings, fits here.
Media- People who kill and then, say, send in letters to attract widespread media attention. Jack the Ripper or the Zodiac or BTK probably fit here (though maybe with elements of some others, like thrill killers).
I mentioned Ed Gein, but I'm not sure he fits any of these. He seems closest to the first, but I'd say his mental and emotional development was so stunted he basically just didn't fully understand the implications of his actions. More like a general type of severe disorder or disability.
I'd call those motivations pretty diverse. Many of them are basically the same motivations normal people have for other things in life. I dunno if it's insane to guess, if your normal restrictions of morality were unshackled or your mental state was a bit more unstable, which is most likely to be the one that rages most out of control.