Search is an important part of social media as it enables anyone to connect with more people. Do you want to be found by a high school or college friend who is looking for you? Or is it more important to you to keep that private? It's best to make it a conscious choice and set up your profile the way you want, rather than leave it to the default settings. The default is usually that some of your profile information, like your name and main photo, can be searched on the site and in Google or other search tools as well.
Facebook allows you to make two choices: who can see your profile when they search for you within Facebook (you can choose "Everyone," "Friends of Friends," or "Friends Only"); and whether or not your profile appears in public search results (like Google) - you can choose yes or no.
To know what to decide, ask yourself why you are on the social network. If it is a professional networking site like LinkedIn or you are job hunting, you will make different choices than if you are primarily interested in socializing with your good friends and family. If you want a smaller, more closed group, consider using a more focused networking tool like Ning or Meetup.