Before you put your tiny diary online, it's important you decide how much privacy you want to keep. When you're sending out messages into space, you might forget people are reading them. Twitter lends itself to a more laidback and personal writing style, so it's important not to be seduced into revealing more than you're comfortable with.
The default setting for Twitter is to allow anyone to follow a feed. If you only want friends and family members reading your updates, go into the preferences and change your settings. And just because everyone else seems to have a headshot on their Twitter pages doesn't mean you need to have one.
There's no right or wrong answer to how much privacy one should keep on Twitter. Choose the level with which you're most comfortable. Many people make the mistake of letting down all privacy guards, using their first and last names, talking about their community and posting pictures of their kids, assuming only a few people will follow them. But once you start following other people and commenting on their tweets, your list of followers will naturally increase. Anyone following that person can read your comments, click on your name, and head straight to your page.
The interactive nature of Twitter is one reason that it has become so popular. It's easy to forget, however, that your comments can be read by anyone, not just the person you're replying to. Many people are surprised how quickly their list of followers grows, without their making any effort to attract followers. If this makes you uncomfortable, change your profile settings before you make your first tweet.