If you're not sure about the harmonica type, start with a standard 10-hole diatonic. You can't go wrong with the Lee Oskar Major Diatonic or the Hohner Special 20 (preferably in the key of "C"), both are great for players just starting out.

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.