I'm going to answer off of the assumption that you are intending to use the microphone for singing and not "mic'ing" instruments.
There are a number of factors to consider when purchasing a microphone, such as, Will you be recording with this mic, or is it for stage use? How much money can you afford to spend? What kind of music are you going to sing? Do you want/need as close to perfect reproduction of your voice as humanly possible?
Some of the questions are answered by type of microphone. There are basically 4 kinds of microphone, (Dynamic, Condenser, RIbbon, Piezo) and 4 kinds of polar patterns (A polar pattern is the area which the microphone is designed to focus on picking up. They are Omnidirectional, Cardioid, Hyper-Cardioid and Figure 8) Each one has its particular drawbacks and benefits.
The Dynamic microphone is typically used for stage. It can be hand-held and typically comes with either a Cardioid or Hyper-cardioid Polar Pattern. These patterns are chosen for these microphones because they tend to pick-up the sounds most directly in front of them and reject sounds from other locations. This is extremely helpful onstage since you don't want to have to compete with the entire band just to be heard through YOUR microphone.
The drawbacks to the Dynamic microphone (as compared to other mic types) are its lack of sensitivity and its lack of range (Range is a microphones' capability of picking up sonic frequencies)
The sensitivity factor is difficult for me to explain, but because a dynamic microphones' diaphragm is heavier than other microphone types, some of a singers' softer, breathier noises and overtones get lost since they are not strong enough to move the diaphragm. (Roughly)
The Dynamic Microphone typically has a range from 100hz-16khz, whereas the human ear can, on average, hear from 20hz to 20khz, so it also can lose some frequency.
(However, the soundwaves in these sections are not always necessary for a good portion of songs, since the 20hz-100hz section of music basically comes of as a deep rumble and the 16-20khz section is a high hiss.)
The condenser mic has an electromagnet in it that is powered either by phantom power (common) or batteries of a breakout box (Much less common) This setup causes the diaphragm to be much more sensitive and receptive to more frequencies, thereby providing a much more realistic and clean sound. Condenser mics come in all polar patterns, many of them can switch between polar patterns with a flick of the finger.
However, due to their high sensitivity and open designs, their susceptibility to feedback and their basic fragility, they are not recommended for stage shows.
Ribbon mics are easy to think of as more highly refined condenser mics, however most ot them do not require power and can even be destroyed by phantom power. Ribbon mics tend to be pricey, but there are some low-cost brands out there. Ribbon mics have lots of uses and are very decent for all-around recording, frequently shining on vocals and piano/guitar. However, they are more fragile than condenser mics and more expensive to repair when they break. (Don't bring a ribbon mic on stage!)
I personally would only recommend ribbon mics to experienced studio owners who have the money for the mics, the repairs and the kind of preamp stages that will make a ribbon mic shine.
Ribbon mics are usually figure 8 or cardioid in design, but they can be made for any polar pattern.
There are also piezo mics, but they are typically not used for singing or recording because of their tendency to sound a bit "honky". They are now being used mostly for acoustic guitar amplification.
All of that aside, I would recommend the Shure SM58 microphone as a beginner mic. Its around $100, its rugged, good quality sound for the price and hard to go wrong with. Plus, it keeps its value well. A used but well taken care of SM58 can typically sell for $60-$80 even after several years have gone by.
It is a dynamic mic and has been tuned to work very well on vocals.
I hope you have enjoyed this microphone mini-novel. (Whew!)
Good luck!!!