Get the rights to the movie. If you cannot secure the rights to show the film inside your film, then get the rights to a smaller film, such as and independent film. Find another filmmaker that you know and secure the rights to his or her film. It may be much cheaper than getting the rights to play a film such as Goodfellas or other movies that have large studios or production companies behind them.
If your film falls beyond the area of a mere school assignment or class project, it would be beneficial to get rights to show a copyrighted film, ESPECIALLY if you plan on sending it to film festivals. What happens if a Film Distributor or TV network is interested in showing your film on their channels? You would then have to go through all of the legal drama just to get rights to show someone else's film in your movie.
It's always best to get all of the rights to footage that you do not own upfront.