One way I typically decide whether or not to use dependency injection is whether or not I need to mock or stub out the collaborating class when writing a unit test for the class under test. For instance, in your example you (correctly) are injecting the DAO because if you write a unit test for your class, you probably don't want any data to actually be written to the database. Or perhaps a collaborating class writes files to the filesystem or is dependent on an external resource. Or the behavior is unpredictable or difficult to account for in a unit test. In those cases it's best to inject those dependencies.
For collaborating classes like TreeSet, I normally would not inject those because there is usually no need to mock out simple classes like these.
One final note: when a field cannot be injected for whatever reason, but I still would like to mock it out in a test, I have found the Junit-addons PrivateAccessor class helpful to be able to switch the class's private field to a mock object created by EasyMock (or jMock or whatever other mocking framework you prefer).