Microphones have what is called a polar pattern. It dictates the area in which the microphone will focus upon when recording.
A cardiod polar pattern is a heart shaped recording range which will focus upon frequencies coming from the front and some side sounds, but tapering around the back. Picture the top of the heart as shooting out from the microphone and a little behind, and the bottom of the heart going toward the stage or source of input. This limits the amount of background noise that is heard when recording at large venues.
A hypercardiod polar pattern is similar to the cardioid pattern but allows a little more sound from behind the mic’s point of reference to filter through. The hypercardiod is more so used for vocal recordings, and are usually noisier than cardiod mics for live music recording.
Omnidirectional microphones are not recommended for recording live music at all. These mics will record in all directions equally, thus reproducing a lot of unwanted crowd noise.
When choosing a microphones frequency range, you are deciding on what frequency will be accepted by the microphone. The human hearing range is from 20hz to 20khz, and so this is the recommended range for a recording mic for live music.