Consider your needs when selecting mics. Do you want perfect sound for recording or do you just want to amplify your sound a bit onstage? For recording, you will need a mic for every drum and quite a few cymbal mics to get the best sound. Onstage you may choose fewer mics but understand that the non-miked drums may not come across in the mix.
Do not skimp when it comes to your snare mic and your bass drum mic. These two are going to take the biggest beating and you want to have the highest quality you can afford. From Audix, the I-5 is a specialized snare mic and the D-4 and D-6 mics are for bass drums.
For your rack toms, Audix has a few choices. For economy, the ADX-90 will provide adequate sound and ease of installation but may not sound great on toms that are very deep in sound. A better choice, if you can afford it, is the D-2 series which will pick up the low frequencies better. For floor toms, go with the D-2 or even the D-4 for seriously deep floor toms (18 inches or larger).
Invest in at least two cymbal mics but you will likely need three or more depending on your set up. You will need one on your hi-hats and also near your crash and ride. The more mics you add, the more accurate your sound will be, especially in recording. You may not need to mic every crash and china in live situations if the club is not too large. When in doubt, use more mics. Try the ADX-51 for a solid cymbal mic.
For your snare, rack toms and floor toms, Audix makes a great device called the D-Vice. It clips onto the rim of your drum and the mic slips right in place. They feature a flexible arm that allows you to position the mics out of your playing area. Try positioning the mics on drums to the left in the 10 or 11 o'clock position and the mics on drums to the right around 1 or 2 o'clock. This will likely keep them out of the way of your drum rolls.
For cymbals, you will need a mic stand for each mic. Boom stands will allow you more flexible placement options. Place one directly pointing at your hi-hats, one in the area of your ride, and any extras floating above major groups of cymbals. You will not need a mic for each cymbal but remember the more you have, the more accurate your sound.
For the bass drum, you need a low profile mic stand that can be set up low to the ground. If you have a ported bass drum (it has a hole in the resonant head), slip the mic into the hole for the best sound. If you do not have a hole, put the mic somewhere off center. If possible, consider porting your resonant head as this is the only way to truly capture the sound.