I tend to view Armageddon MUD as a kind of weird hybrid of method acting and improv. Hence, characters for me will start out as a personality or a bundle of personality quirks first and foremost, and then develop (including developments in terms of family history) as I go about bumbling around in the game. What I tend to do is write a really sparse background, since I'm really unsure about the character until I see it play out; but within the first week, I'll write up an initial biography entry outlaying their personality quirks and filling out this background in a little more detail.
Where do I get inspiration? All over the place: a character in a TV show or novel whose personality you think might be fun to try out in Zalanthas; that crazy woman on the street you passed who talks to pigeons; some coworker, a colleague. I almost invariably have a RL persona (or several) that I use. This helps keep me grounded, and prevents my personality from shifting too far from the original concept.
Sometimes, however, I come into the game as a blank slate with only the vague-est idea of what I will be, and wait for another PC to come around, and I'll just develop the concept on the fly.
The most important thing for me, though, is to document the personality in BIO entries (or on a notebook) once it gets solidified enough. It is too easy to be too flexible, and having hangups and quirks --- immoveables, furniture in the barren ontological landscape of the psyche --- really helps make the RP experience a blast.
Finally, one thing that I always have square in front of me is that I might just die within a few days or weeks, and in case, I will die. This is a game, and it is fun to make your character have personality quirks that will get them dead, or at least get them engaged in conflict.