Decide which type of directional pattern best fits your needs. Remember that it’s usually better to use a less directional mic in a position close to the sound source, than to be further away using a hypercardioid. For more information see microphone directional characteristics.
Make sure the mic’s frequency response is appropriate for the intended use. As a rule of thumb flat response patterns are best, but in many cases a tailored response will be even better. For more information see microphone frequency response.
The rule of thumb is: Low impedance is better than high impedance. For more information see microphone impedance.
Remember that the diaphragm works by converting vibrations from sound waves into an electrical signal. Unless the microphone has some sort of protection system, the diapragm can’t tell the difference between a desirable sound wave vibration and any other sort of vibration (such as a person tapping the microphone casing). Any sort of vibration at all will become part of the generated audio signal.
If your mic is likely to be subjected to any sort of handling noise or vibration, you will need a mic which will help prevent this noise from being picked up. High quality hand-held mics usually attempt to isolate the diaphragm from vibrations using foam padding, suspension, or some other method. Low quality mics tend to transfer vibrations from the casing right into the diaphragm, resulting in a terrible noise.
Note that lavalier mics don’t usually have protection from handling noise, simply because they are too small to incorporate any padding. It is therefore important to make sure they won’t be moved or bumped.