Of all the games I've actually played, Phantasy Star Online 2 by far had the most robust character creator and is F2P, though region-locked (But easily bypassable).

You're pretty much guaranteed to be able make the exact sort of face you'd want, and while the body options aren't as robust, they're still unlikely to disappoint, being able to alter limb length/width, muscle tone, and weight to get a build that should be fairly close to what one wants.