You're allowed only to have one private profile page, now called timeline. In addition to this one profile page, you can have as many fan pages you want and you can open as many groups as you want as well.
To keep the different sites on Facebook separate, your profile page needs to connect with friends through friends requests, while a group or fan page only need people to LIKE your page, no friend requests etc needed. If people like your page, all they need to do is to click on the like button :o)
Here's our fan page:
https://www.facebook.com/pages/Always-An-Adventure/189237974431755