Sparrow, are you sure your songs are in a playlist? When I play songs sorted according to "artist" or "album", it will go back to the menu after that song or album has played, but if you organize them in a playlist, it won't, or shouldn't, go back to the menu until every song in that playlist has played. Is that clear as mud!? LOL!!!
To make a playlist, you drag songs from your main music library into a playlist on the left of the iTunes screen.