I'm not necessarily set on having the slogan included.
I'd certainly be using this on facebook. I'd likely put the full logo and words across the top on the banner, but I'd also like to make the "logo" portion the profile picture, and I would like that picture to be obvious that it's a running related logo.
The demographic will primarily be women, however I think that a logo designed specifically towards women would end up excluding a large part of the target audience. I'd prefer to see gender neutral logos, or logos that wouldn't necessarily exclude men.
I'd also like to see logos that show versatility. Some examples I've seen that I like are logos that are recognizable as silhouettes, logos that lend themselves to different color options depending on event colors, or logos that have some alternate pictures available such as a male or female runner, or a single or pair of runners.
I've been liking, and seem to prefer the runner logos with a slower feel of a casual jog, where the runner is landing on the front foot with the back leg extended back. If you search for "chi running" or "pose running" you will see good examples of what I'm trying to describe.