Facebook settings can get rid of all unwanted posts and messages.
When you get unwanted attention use the Report/Block button and you will not see them again - I have to hope that if enough people report a user Facebook will take some action. Trolls feed on attention ignore and they go away.
Next thing is to set the privacy settings so that only Friends can post on your wall or tag you. You either use the quick "Friends" privacy settings or use custom settings and decide on individual settings.
If you leave the front door open don't be surprised if someone undesirable wanders in!