It kind of depends on what your purpose is, what your image is, and whether you’re representing yourself or your gym. I do the social media for one of the clubs where I work and that’s much more formal than my own social media.
My photographs and videos:
I do quite a few informal shots of my classes, because that gives potential clients a feel for what my classes are like. My class atmosphere is fun and informal (although professional and well-planned). Informal shots on a regular basis showing my clients’ progress is motivating for those clients to be shown doing something great. I rotate which clients I photograph and post, to give everyone a nod now and then, plus that shows off my client demographic.
I do have one professionally shot one-minute clip of myself being interviewed, which is the front page video on my youtube channel and I put it on fb every 4-6 months. That’s really all I’ve done professionally, but it’s gotten quite a lot of views.