(See? We told you it would seem obvious.)
There are a number of ways in which you need to attend to what you write about yourself and your work though. Just like a CV there are different things to cover: introducing yourself; listing what you have done; talking about your capabilities, interests and availability. Perhaps you might want to write a news feed or a blog - just like the column on which you are reading this post. This may demonstrate the way in which you think professionally, or even show that you bring more to (say) an opera role than your vocal technique.
All the time remember that your writing style, not to mention accuracy - spelling, grammar, correct spelling of names and use of diacriticals (accents) - give an indication of your attention to detail. Or simply just how much you care. Make sure reviews & quotes are accurate and properly attributed. Wherever possible link to the original online piece from which a quote is taken.
Two things. Firstly, a good, clear, high resolution headshot is important as a focus point for advertising and also for programmes if you are employed as a soloist. Make sure your headshot is reasonably current (e.g. don't use a picture with a beard if you've shaved that off) and that it reflects who you are. Try not to make it fussy - it will become either distracting or may be inappropriate for some gigs.
Secondly: do try and get/find pictures of you doing what you do. Perhaps a friend has taken a picture of you at a curtain call. Or even in action. Have a look online - perhaps someone in the audience has taken a snap of you and shared it ("i went to this awsum concert check out the amazing singer lol" [+ image]) is not as rare as you'd think. (For example, here's a flickr account for an opera-goer who loves taking photos of curtain calls - and many high-profile artists are grateful in return)
3. Audio. You can spend as much money as you like on lovely studio headshots (hey, you're worth it) but remember, the audience come to hear you sing - and more importantly, those who might employ you are principally interested in how you sound. These days its fairly straightforward to buy a voice recorder and set it up discreetly at the back of a performing space. Still, you might want to get a professional recording done. Whether it's in a studio or in a performance space, make sure the acoustic is fairly clear.
We were at a singers' forum in 2012 where an agent despaired at websites with galleries with dozens of photos but not a single audio clip to listen to. Don't neglect this.
4. Video. Video is ubiquitous nowadays. Good video camcorders can cost less than a voice recorder. Even HD video can be recorded on a smartphone and (roughly) edited on an app. The audio feed on smartphones and video cameras tends to be less good but the opportunity for a client or an audience to see you doing what you do is valuable. Tips
- Read what you write about yourself out loud. Get someone else to read it for you. Try not to use contractions or acronyms without writing them in full once, first (eg. "... worked at Welsh National Opera (WNO). Also for WNO...)
- Check your links. Just as you keep your CV up-to-date make sure that links have not become obsolete over time.
- Permissions. Credit third parties who take photos or record audio or video for you. Always make sure that the pianist/orchestra/conductor with whom you are working is alright with you recording something for personal promotion before you even set up the devices.
- Don't use rubbish media (poor quality recording or you singing flat) simply as it's all you have.
- It's difficult unprofessional to selfie (yes, I'm using that as a verb!) at work. If you've got a supportive friend who wants to hear you, get them a comp and ask them to press 'record' before you perform or take a photo afterwards.