If you wish that a particular person not be able to access your profile or even see that you have a Facebook account, there is a "Block Lists" in the privacy section (note that all unless otherwise noted require going into the privacy section). Just enter the name of the person you wish to block. Note that for this that the person can log on under another ID that would enable him or her to access your profile according to your privacy settings.
Under "Customize Settings" in the privacy section there is a section "Things Others Share". This is what others can share about you. Make sure to edit these to your choosing. In particular "Friends Can Check Me Into Places". This is one that you will likely want to disable. For "Photos and Videos I'm Tagged In" you will likely want "Friends Only" or "Only Me" which is under "Customize". For "Suggest Photos of me to Friends" I would suggest you disable this. Friends can tag you without suggestions.
Be very careful about sharing contact information. I would not share phone numbers and addresses with anyone within Facebook. Those settings should be set to "Only Me". Personally I did not enter any information for them. For email addresses if I was to share I would only share with friends. Unless there is a business reason I would not share beyond. If you have a website, you can share that with everyone. Anyone can see the address of this blog as well as my Twitter account. For Twitter the privacy setting is under "IM Screen Names".
You also want to be careful about what Apps and websites share about you. In the "Apps and Websites" section under "Info accessible through your friends" I would suggest under "Edit Settings" you keep all unchecked. For Public Search, you need to determine whether you want your profile to be found when a search engine is used. Select as you see fit.
Facebook is a great site for social connections and for reconnecting with old friends. With the privacy issues that Facebook has had and will likely continue to have, you need to keep on top of your privacy settings. As always, be careful of what you put out there. You never know who will see it. For starters divorce attorneys have been known to go through Facebook profiles to aid in their cases. I heard a story of a divorce attorney friending their clients estranged spouse in an attempt to get incriminating information. Now of course the estrange spouse should never have friended the attorney but that is another story.