Everything not included in the class's interface should (must, really) be private. If you're not sure what the class's interface is (i.e., you're not http://www.artima.com/lejava/articles/designprinciples.html>programming to interfaces or those interfaces aren't yet fully defined, start with everything private and make things public, protected, package-private, etc. as needed.
But think carefully! Once something is accessible to other code, there's a dependency between that code and this class and refactoring is constrained. Rule of thumb: Expose only those methods that define the abstraction, not how it's implemented.
