Getting a facebook page if fine, just NEVER set it up using your real name, and never, never, give it your address, phone numbers, place of employment, school, or any type of financial information. It will ask for this information when you establish your account, but you do not need to provide it, and should not. I'm not saying to lie about this Information, just don't provide it. Its not necessary to have an account. Set it up using an alias name, and give your close friends and family your alias. You have an alias here on Yahoo, do same on Facebook.
Every few days their security policy and procedures change. What they tell you will be private and confidential information today, will be published for the world to see tomorrow. Actual Example - millions of people signed up, provided their real phone numbers, were promised by Facebook that this was confidential and secure information, would never be published, and one day they log on to find their phone numbers posted for the world to see. NEVER TRUST FACEBOOK WITH ANY REAL INFORMATION ABOUT YOURSELF OR YOUR FAMILY. It can all be accessed by anyone with just beginner hacker skills.
If you already have an account, and you provided all that information, go back into your account NOW and remove all you can.
Do not "friend" of "like" anyone, or any site, you're not sure of, and who you don't want to have access to your page.