I'm still not too sure I've really got the categories down, so I've decided to rate two well-known fictional characters as though they were SCPs. Please note that I am not any way, shape of form advocating that these be made actual SCPs! This is solely for the purpose of getting a better handle on the SCP classes.
First: Jason Voorhees.
Reasoning: He's a purely physical being. He's immensely strong and tough, yes, and he won't stay dead, yes, and he's a murderous nutjob, yes. But at the same time, he has an agenda that determines his actions (he acts to punish "immoral" behaviour), he can be defeated by two or three ordinary teens if they keep their wits about them, and can be kept contained in any reasonably tough cell. He has no morphic, variable, or unrevealed powers. What you see is what you get.
Second: Freddy Krueger
Reasoning: He's a master of evil dreams, lord of nightmares, and seeks nothing beyond the spreading of pain, suffering and death. Within his own domain, his powers are all but limitless, and because he has no physical presence, containing him is nearly impossible; the only ways ever shown to do it are to keep the Elm Street kids from dreaming, or to keep his story going in its original, unaltered form, thereby confining him to that story. Permanently destroying him seems to be impossible. He's not even limited to that one Elm Street. Granted, a given individual can strip him of his power to harm her by overcoming her fear of him, but this is not a viable strategy on the large scale.