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.

With regular deliberate practice, you can expect to be playing simple pop tunes within around 3 months. Within 6 to 12 months, your technique will improve and you will probably be able to work on bending notes (a very important skill for getting the best out of a harmonica).

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.