It seems that I have to choose the copy to hard drive option rather than the ripping option. After copying, there are two folders: AUDIO_TS and VIDEO_TS. Inside VIDEO_TS, there are files with .ifo, .vob, .bup extension. Which one gives me the menu option?
If you did the Full Disc Copy, Drag the top level folder (the folder containing these two: video_ts and audio_ts) to DVD Player. It will play the menu like the DVD.
Also, you can now rip mp4 from these folders in the future, instead of from the original disc.