Choose a large diaphragm dynamic microphone for use on the kick drum. Popular microphones for this task are the AKG D112 or Shure Beta 52. Large diaphragm dynamic microphones excel at capturing the low-end frequency content. They are also durable and can withstand the high sound pressure levels generated by a kick drum without distorting.
Choose a small diaphragm dynamic microphone with a cardioid pickup pattern for the snare drum. Popular microphones for this task are the Shure SM57 or Audix i5. These types of microphones tend to boost the presence of the sound they capture, which helps the snare to really "pop." Also, the cardioid pickup pattern helps block out the hi-hat, cymbals and tom-toms surrounding the snare. The ability of a dynamic microphone to handle the high sound pressure levels generated by the snare drum is also important.
Choose a small diaphragm dynamic microphone with a cardioid pickup pattern for the rack (high) tom and choose a large diaphragm dynamic microphone for the floor (low) tom. As you would expect, the rack tom microphone will enhance the attack of the rack tom while blocking out external sound. The floor tom microphone will enhance the low end of the floor tom, while withstanding the high sound pressure levels it develops.
Choose two condenser microphones for overhead microphones. These microphones will capture the drum set as well as the cymbals. Dynamic microphones will not work well for this purpose, as they tend to de-emphasize the high end and make the cymbals sound dull. Popular microphones for this task include AKG C414s, Shure SM81s and Rode NT5s. Condenser microphones especially excel at capturing the rich harmonic content generated by the cymbals. Their frequency response also represents the sound of the entire drum kit well.