I don't really have an elaborate PROCESS for liking characters. I mean, seriously, I'm not some kind of machine. I just like characters when I like them.
That said, I like a wide variety of characters. They usually have to impress me in some way (similar to real people). Take Dio Brando, for example. I never thought I would like a completely evil character like Dio, but I did! Though I guess in the end, I have an affinity for holy men and honourable warrior kinds. And gentlemen, can't forget them.