Selecting the right Mics for a live drum recording can be a difficult decision. Drums tend to have an unique sound for each individual kit. You also have to take into consideration the style of drumming. The drummer is just as much a part of the kit, so based on how the drummers plays the recording of the kit should factor in to your decision.
Overhead mics are by far an important decision you make when deciding to record drums. A decent amount of your audio will come from the overhead mics. Overhead Mic placement is also a big factor whether you do a symmetrical or asymmetrical mic placement. Just make sure that your mics are placed equidistant from the snare drum so that you don't have any phasing problems with your snare sound.
Condenser mics are usually the first choice for overhead mics on a drum set, however many engineers have had lots of success using dynamic microphones for their overhead mics (OH). The goal is to capture the essence of the drum kit. Putting the drums in the mix to set the mood for the music is the goal. How you sculpt your sound will define your ability to record and mix a quality production.
You can always place mics and then decide if they are relevant to the mix. Just watch out for phasing and over-ambiance. The more mics in the mix, the more likely you'll have phase problems or what I like to call a foggy mix. Try starting your mix with just the overhead mics and mute all other mics. Listen to what the OH mics are providing and then slowly bring in the other mics. You should filter and EQ each mic so it fits in with the OH mix. If the signal is weak or disappears, then invert the phase to see if the track is out of phase with the OH track.
There's more to cover, so I'll open this topic up for questions and discussion. Leave a comment below to add any insight you'd like to share.