I recommend you start with a harmonica in the key of C for several reasons. Most importantly, a C harmonica will enable you to be in tune with the majority of beginning level harmonica lessons.

Start with C Major as it has no sharps or flats, then G D, A and E major before starting the minors. Next, learn some pentatonic, blues and chromatic scales plus the modes.

A mouth organ has 2 reeds per note with a set vibrato. A harmonica has 1 high quality reed per note that allows the player to create his own vibrato at a speed that suits the music being played. The harmonica also has a chromatic lever on one end, which means that you have the sharps and flats.