Do you ever write characters before a story?

Recently I just wrote a characters physical appearance and started jotting down points about the character, I've done a few of these before but never have I started off with the appearance.

The initial note I wrote: A Greyhound-like character with a sleek and slender build, long, narrow face, pointed ears, deep chest, wearing a short, smooth coat, graceful gait, athletic movements.

I normally write with a theme in mind not a character, so the characters I write often feel forced into the story.

I'd love to hear what you feel makes a character apt for a story and what order you tend to build a story in.