I was thinking about making a small project that would light up an LED if the noise recorded from a microphone was loud enough. I did a Google search and I didn't find much about what microphone I should use, I wanted to know which one I might want to use for this project and what its pros and cons are.
popa
i cant tell you much from a arduino standpoint as im a total newb. But I can telly you from a sound engineer standpoint condenser will require 48volts (phantom power) and a pretty good preamp, it will sound alot better but will be harder and require more space as their not that small of a mic.
electret is pretty low power and doesnt sound that bad for what it is. and it will be alot cheaper. i would personally go with electret if youre not planning on doing any important recordings with it.
Technically, it's an electret condenser mic.
All condenser microphones require power. As florios said, "studio condenser" mics require 48V. Most "performance condenser" mics are actually electrets and they can optionally use a battery. The mic input on a soundcard is designed to supply power (5V) to an electret condenser.
Dynamic mics are made like a speaker with a coil & magnet and they don't require power. (The most popular mic ever, the Shure SM58, is dynamic.
A microphone puts-out a tiny signal, usually less than 100mV, depending on the microphone and the loudness of the sound. You need a preamplifier to bring the signal up to at least 1V for the Arduino or to drive an amplifier. The Arduino's ADC has a default range of 0-5V, with an optional 0-1.1V range.
The easiest solution is to get [u]this board[/u] which has the mic and amplifier built-in. Note that the Sparkfun board is biased at 2.5V so that the Arduino can read the positive and negative halves of the audio waveform. That means silence will read about 512 (with the default 5V ADC reference) and loud sounds will result in bigger and smaller readings.
Note that when you read audio waveforms, you are reading "random" places along the wave. It's like measuring the height of ocean waves... Big waves will give big numbers but they will also give you small numbers and negative numbers (if not biased), and a big wave will read zero at the zero-crossing. So if you want to read "loudness", you have to throw-away everything except the peaks, or you can take a bunch of readings and average them. But since the wave goes negative, the mathematical average will be zero, so you have to take the average of the absolute values or throw-away the negative readings. (With the 2.5V bias, the mathematical average will be 2.5V = 512 on the ADC.)
I was thinking about making a small project that would light up an LED if the noise recorded from a microphone was loud enough.
With some creative programming involving a circular buffer, you can create an effect where the LED/lamp comes on whenever the sound is louder than average and goes off whenever the sound is quitter than average. That way it automatically adjusts for quiet sounds or loud sounds and you are always getting lots of "LED action" without adjusting anything. I have a lighting controller and one of it's effects is based on this concept, where I keep 20 second moving average. (Search for the "Smoothing Example" if you want to make a circular buffer.)
if the noise recorded...
FYI, some audio terminology - "Noise" is unwanted sound. 
Hum or hiss in your audio/recording is noise. If you are recording yourself singing and your dog is barking, the barking is noise. Or if your Mom doesn't like the music you listen to, she may consider it noise! 
And if you are "recording", that usually means you are capturing and storing the sound for playback later... Just like a video camera records video.
Thank you DVDdoug, earlier today I was looking in Sparkfun and decided to order that mic.