My process starts with figuring out what the character will be doing. The most interesting PC in my head is useless if there's no way to utilize them in the actual game; how will he interact with others? What makes him interesting for them to play with? What can he do in a group, why would other people go to him? What would his preferred role be in plots?
If the game supports distinctive factions and/or templates (Bloodlines, Legacies, etc) I definitely look at that at this stage as well. While it can be fun occasionally to shoehorn the 'wrong' personality into an archetype they're not a good fit for, it takes some special circumstances to make it happen. If that's the path I'll choose then it needs to be part of his progression (starting with a peace-loving bookworm who's shaped by in-game tragedy to slowly become something else), but since that can take a while I'd reserve it for games I expect to be playing long-termly.
I have some idea of those things before I enter CGen since it's then that I figure he's functional. A bookish loner is no good though, even if his stats could make him useful for others, so that's when I start gearing his background in my head - the guy needs to either want or be compelled to be social to some degree. At this point I know about what his skills and attributes should be geared towards, so I pick them and move on as soon as possible to the next stage; the background.
I don't like making characters with a very wealthy history. It can easily lead to a too-cool-for-school IC outlook which I abhor; the guy should never look at in-game events and go 'meh, I've seen worse' just based on his past unless that's somehow interesting on its own (and it rarely is). I prefer thinking of those as foundations for the future, stuff to build on - maybe he's seen some shit but he's not prepared for this. Or he has seen even worse yet now he needs to re-interpret his role and carve a new place in the world (which may not let him)... but there should be a wealth of options in there I can use to propel him forward. The worst case scenario here would be a stagnant character whose potential is capped by his own background story.
I freely admit I don't have any idea who a new character is during the first few sessions with him; I know what he is but his personality is under development. It's taken me anywhere from one to... many scenes before I went hah! and found a PC's voice when he allowed me under his skin. I sometimes read my own logs weeks or months later and I laughed because it was basically all wrong, but that's just a byproduct of this process. I start generic, try things out, probably make him more irritating or know-it-all than he tends to become later on, but it's never right off the bat.
I also hate redoing things I've already played. It feels like a failure if I have a 'type' that I like. I'm already prone to making characters who talk a lot because that's just my style (I know, stop gasping) so the last thing I need is to also play the same personality over and over again. Not that there's anything inherently wrong with it, but I'd like to think I can pull different things off.
Finally... I don't like making characters who're too... in-your-face with their weirdness. I do like them being strange but not when it's anywhere near Fishmalk levels; there need to be subtleties, intricancies, stuff you don't see at a first glance. The character can be flawed as hell but I don't like that being in your face. I also enjoy playing them the less likable types sometimes; the idea everyone I play needs to be super liberal, free-thinking and fair doesn't sit well with me. They don't need to be assholes - people should still like them - but not perfect.
As for the appearance... I can't say I work on it too hard. I used to like artwork, but it's fallen out of fashion so I just pick someone who looks appropriate, but it's an afterthought at best for me.