There's no such thing.
Think about it, let's take two people, both recent college graduates, one wants to be invited to the best parties and one want's to go work for IBM - there's practically no single style of photo that would work for both of those.
The first person would want a picture of himself in a wild party, the wider the better - but that picture won't earn him any points with the IBM recruiter.
The second person should probably go for a simple headshot-ish picture in an appropriately nice shirt against a flat background (see my picture at the bottom of this post, my day job is in software consulting so I use a bland "professional looking" image) - this picture will make the party friends call him a mildly insulting names and move on.
This is actually a marketing question, not a photography one, It's like asking for rules for logo design that will work both for dell.com and mailchimp.com - they just want to convey such a different message it's hard to find any common ground.
What does the person want people to think of him/her? what picture will best represent this person they way he/she wants?
The persona doesn't have to be separated from the background (sometimes an environmental portrait style is more appropriate), the person doesn't necessarily have to be identifiable, look into the camera or smile, even nice lighting isn't always needed to the convey the "message" the person is trying to get across (but as the photographer it's your job to get the lighting right)
The only rule I can think of that is applicable to a wide range of people is to avoid small details because those can be lost when the picture is downsized and one's profile picture is likely to be downsized all the way down to a tiny icon in multiple places.