You know what they say about first impressions, and your social media profile picture is the online equivalent of a first impression!
Is there such a thing as the perfect profile picture? Probably not, but excellence is the next best thing!
Simply, use your logo in a size to fit into the space! Your profile picture needs to be instantly recognisable, even at fairly small-scale and of good resolution. If you logo is too large or the wrong shape to work well as a profile shot, consider creating a smaller version of part of your logo for social media purposes.
The key is consistency across all your branding. Use the same image as a profile shot across all your social media channels.