I get asked this a lot. Many people go to band auditions or rehersals and either come over prepared and bring a ginormous kit and spend half an hour setting up, or dont bring enough and let the music suffer because of this. When I get asked what I bring I tend to just say "whatevers necessary". If you are going to a band audition, a first impression doesn't start with the playing but with the communication. Make sure you know the style they play so you know how much is appropriate. If they want a hair metal drummer then by all means bring a full kit. But if they say "oh were a five piece folk band" dont turn up with your giant kit. They wont be impressed, more likely think "oh gods an over the top too loud drummer who is taking up the entire practice area with his ego drum kit". I play in a 3-5 piece blues band with variable lineup. Now for practice and my audition I bring the same. I turn a floor tom on its side, bring a snare, hi hats and a crash ride. I then bring brushes and sticks and a pedal. This is all that is needed, and for most auditions this will do too. Even a rock band, because a steady rock beat is what drives a band, and if you can get through a whole set with just this you are more likely to impress them with your versatility under such a restrictive setup. Bringing brushes (in anything other than metal. Seriously even rock) is a MUST. You dont know how loud the band will be, and you dont want to deafen everyone. Plus the proper use of brushes again shows both a willingness to adapt to the bands music and even more versatility in the way you play. Plus it opens up whole new sounds for the restrictive set up you use.
So the big ones are:
1) Dont bring too much or too little.
2) Communication is key!
3) Bring a spare parts bag. This is common sense!
Follow those four steps and good luck on your next audition!
Peace and goodwill!