What comes first, the chicken or the egg? That's the way I feel about how characters occur to me. I cannot think of an instance where a character idea came to me that was devoid of any kind of situation or context. I often have what I think of as a "flash," in which a person plus action/setting stamps itself on my brain in vivid detail.
Sometimes, I have only to turn my attention to the person and their personality and past and possible future come pouring out. Other times, I have to ask the questions: "who are you?" "what are you doing here?" "what do you want?" to help form the character in my mind. A third type of creation comes after an idea. Meaning, a what-if or an event occurs to me, and I have to ask what kind of characters belong with those circumstances. So process really depends on how fully formed the characters and their needs are at the beginning. Perhaps unsurprisingly, characters and their more-or-less complete story arcs occur to me a LOT more easily now that I've been writing for a while.
Under the cut, I've detailed what came first character or plot for each of my WIPs and planned future novels.
These are presented in chronological order:
The Traveler's Daughter - character in a fully-formed setting (not to be confused with a fully-formed world). This character does not appear in the book, nor does anything resembling my tentative first ideas.
The Thirteen Virgins - I don't know if I will ever get around to writing this one, but the POV Diggory flashed into my mind fully formed along with the inkling of plot.
To Be Undone - A what-if. I knew the character concerned would have to be female, but I knew nothing about her.
Alabaster - Working title because it is the MC's name. She and a social aspect of her world appeared to me pretty fully formed, right down to where her name comes from. The plot is still semi-fluid in my mind.
The Bitter River - Two characters in a situation. The characters have remained; the situation and germ of plot will be used for another book. The one I had slotted for the POV is still an MC, but the second character is the POV.
Witherwilds - As I said in a recent post, pretty much everything occurred to me at the same time. It was an instance of having the characters and their arcs there already; I just had to sit back and see how they all tied together and played off one another.
Oh, a thing about the creation process that I used to do to help me define characters was to use Chinese Astrology. Handy for looking at characters in different ways. I did a bit of it for TTD and TBU.