When someone wants to know about someone they are tweeting to, they go to that persons Twitter profile. The Twitter profile has place for a picture and a biographical [bio] section. So first, I would suggest a photograph of yourself. You can use an Avatar image, but your picture from the shoulder up will be fine. An avatar is a black silhouette of your choosing that represents you in this profile.
Now as far as filling in the bio. section, you have one hundred and sixty characters to describe yourself. The good news is you can change this description anytime you want. You can get ideas from looking at other people’s bio. that you see on Twitter.
The reason for going on Twitter is to get people to know you and your business and website. People want to talk to real people and not some faceless corporate logo. I would suggest to take writing your profile seriously, and learn to convey a lot of information in very few words.