I tend to work backwards. Plot first, character second.
Set up a situation, starting with something that seems normal, and then keep throwing muck at the characters until something develops. Even if it’s only a patent medicine.
Except that’s not quite true. I develop something of the background of my characters in order to define the situation. In “The curious profession of Dr Craven,” I knew from the beginning that Dr Craven was a widower, isolated from society by his own guilt over his late wife. Cecelia, started as more of a cipher, a blank slate. Still, she was desperate enough to flee her rather rascally father by marrying anyone she could. Fortunately she meets Dr Craven before too long.
In Frankenkitty Jennifer starts almost as the essential ‘valley girl’ but develops to a clever and mature young woman. The adults in that young adult book are mostly childish, and always clueless. Of course her cat, Snuffles, gets a shot at nine more lives. Though at a somewhat larger scale than he had in his first nine. Gertrude starts as her elderly German neighbor, a seemingly sweet old woman with a soft spot for Jenny. She returns halfway through, her youth restored by the mysterious “pink solution,” as a manipulative man-killer (figuratively).