Bachata is a sensual dance often played at clubs, built around a three-step with Cuban hip motion, followed by a tap including a hip movement on the 4th beat.
Rumba is a sexy, romantic dance that is a very popular way to dance with the person you care about. It has been danced countless times as the first dance of the bride and groom. It is also very popular in clubs when the music slows down and the floor gets crowded.
Waltz is an elegant and graceful dance that'll take around the dance floor. It is generally seen at more formal affairs and is often a first dance at weddings.