Typically I look at what the party needs and work backward from there. Sometimes that means: 'We need a cleric', other times it means: 'We need a straight man' or 'We need a leader'.

If we don't have a party yet, then I'll often look at the DM's setup. What kind of character is going to make his job easier? Someone headstrong to move things forward when they're slow? Someone cautious who will get the party to follow up on details? Someone who has a bunch of knowledge skills or comes from a specific place in the setting so he can justify giving us important lore? etc.

After that I start worrying about how to give them interesting twists and motivations to suit me personally.

I think I may be a bit unusual in this respect. I don't tend to come up with my own ideas out of the blue much but once I have something to work off of then I hit the ground running.