I'd advise doing both.
Keep your FB profile as clean as you can. Nothing risqué, no strong religious or political posts or groups, no references to use of alcohol or other drugs. Even if you think your profile is totally locked down, you never know who's watching, and FB always seems to be changing their idea of privacy.
At the same time, keep it relatively private. I HATE getting friend requests, clicking on the name, and seeing only "John Doe, Sex: Male, 1 mutual friend". (I get at least one of these a week, as I play several FB games. I routinely ignore them.) Let the world see your name, sex, maybe hometown and a few interests (which may spark a conversation during recruitment), and that's it.