Assuming that you're using LWJGL, the Display class is basically the 'GLUT' of Java. Display.create() creates a double buffered OpenGL context with a 24-bit color buffer and an 8-bit depth buffer, so you don't need to worry about any GLUT stuff at all.

Display, Keyboard, and Mouse make up the GLUT replacements.  Note that none of it is event-based like GLUT, you have to poll for input and window events, so any C++ code using the callbacks will have to be switched around a bit.  

GLUT also defines some geometry primitives, including the iconic teapot, but those are very old-school and don't fit in modern opengl.  If you're really jonesing for a teapot, I did get around to porting the one in JOGL, but I'd recommend going with a VBO version of the teapot and working with that instead.

You need an FBO (or the deprecated PBO) to do shadow mapping.