The great variety of microphones available through eBay is truly dazzling, so where do you begin? As with any musical equipment, you first should ask what you need a mic for, and then match the microphone to that need.
 POLAR PATTERNS
First, lets talk polar patterns. The polar pattern tells you where the mic will best pick up sound.
CARDIOID (pronounced "CAR-DEE-OID") is the most common mic. This means the mic will pick up more sound from the area at which its pointed (the "axis"). As you move off-axis around the mic, it picks up less and less sound. So cardiod mics are great where there's a focussed sound you want to pick up, but lots of other sounds around that you don't want to pick up. So for vocals on stage, this may be the mic for you.
HYPER-CARDIOID is just cardiod on steroids. It has a narrower axis, so sounds starts getting rejected sooner as you move off-axis. This is the mic for you if you have lots of sound sources close together, like a drum kit, and you want to try and isolate just one of the sounds (like the snare drum) as much as you can.
OMNI is easy. It picks up sound equally well from all directions. You use this sort of mic when you want to get the ambience and feel of a performance, complete with all the lovely echoes and surrounding sounds. You can also use it to record large groups with just one microphone.
FIGURE 8 means the mic has two areas where it picks up sound really well - straight along the axis, and directly backwards (180 degrees) from that. However, it has sharp notches, where it hardly picks up sound at all, at its sides (90 degrees and 270 degrees). This pattern allows you to mic a sound, like a guitar amp, and pick up some of the room feel (the reverb or ambience) at the same time, but still rejecting other sounds coming in from the side. It gives a more natural and open feel than a cardiod, but that backwards pointing area of sensitivity has got to be watched so that no unwanted noise creeps in.
VARIABLE PATTERN mics have a multi-position switch or dial that allows you to set the mic from omni to cardiod to figure 8. The choice of pattern makes them versatile, but it comes with a price tag attached.
 MIC TYPES
There are four main types of microphones.
DYNAMIC mics are speakers in reverse. They have a cone and magnet that moves back and forth with sound vibrations, and a wire coil converts the movement of the magnetic into an electronic signal. For the most basic mics, thats all there is to them. However, better mics add in a transformer or other circuitry to "balance" the output and make it suitable to send down a long mic cable without losing or degrading the signal (the fancy word here is impedance). Dynamic mics tend to be sturdy, providing a moderate signal level to your preamplifier, and perhaps better in the lower to mid frequencies (bass, drums, vocals) than in the higher (cymbals, triangles, etc). They typically are cardioid or hypercardioid in pattern, but you can get them in omni as well.
CONDENSOR mics use a metal plate, usually gold, separated from an electronically charged back plate. They are more sensitive than dynamic mics because there's no such much mechanical pushing and shoving going on, so they have high signal output and a wider frequency response. The big issue is that they need some external power source - usually 48V "phantom power" that is sent through the mic lead from your mixing desk or preamplifier, but some can work with batteries. The way in which the back plate is charged allows condensors to be come in just about any pattern you can think. Multi-pattern mics will be condensors.
Condensors come in many different forms. The major divisions relate to how the signal is amplified within the mic (tube =warm and fuzzy, transformer=not so warm but not so fuzzy, or transformerless = clean and clear) and the size of the gold plate ("large", about 1 inch, which picks up wider, more ambient sounds like vocals, room sounds or small "pencil" condensors, generally about 1/4 inch, that pick up a focussed sound like drum overheads, or instrument mics for brass, woodwind or high string instruments). With all this choice, its not surprising that people get confused. The most expensive mics are generally tube or transformer condensors - the famous Neumann U47, the AKG C12 - these are the premium mics, but you can buy a car for less money!
ELECTRET mics work the same way as condensors, but the back plate is permanently charged and so the power supply needed to run them is much smaller. These usually run off batteries, and are quite small. Lapel mics are one example. Electrets have an omni pattern. While they tend to be dismissed as "toy" mics with poor frequency response, they can be used very effectively in the right circumstance, especially in combination.
RIBBON mics have a very thin strip of metal (hence "ribbon") vibrating between two magnets. They are Figure 8 pattern. Ribbons give a warmer, more coloured sound and a richer bass than other mics, and are great for miking guitar cabinets, recording vocals, and things like that. They do wear out, though, and have a tendency to be more fragile than other mics, so handle with care. They also characteristically have a lower signal output level than other mics, so you'll need a good preamp with lots of gain (like 70db or more) to run a ribbon mic.
 SO WHICH MIC IS FOR ME?
No one microphone does everything. They all have strengths and weaknesses, so the skill is to use the right mic for the job at hand.
For your first mic, I'd recommend you start with a good, balanced-output dynamic cardioid mic. Good brands include SHURE, AKG, Beyer-Dynamic, Audio Technica, and Audix. A word of warning: the SHURE SM58, SM57, Beta57 and Beta58 mics are very popular, and poor quality counterfeit / fake products are on the market. If buying one of these mics, ensure the seller has a refund policy that allows you to return the mic, and get it checked by an expert as soon as it arrives.
Your next mic should be a large condensor, ideally multipattern, but stay away from tube condensors just for now. The Australian manufacturer RODE has a few available (the NT1000, NT-1A, NT2000 and NT-2A), all of which are good, world class mics. Remember that there is no point getting a condensor mic unless you can power it with phantom power, either from your preamp, mixing desk or a stand-alone box. If you have the money, NEUMANN condensors are probably the most prestigous and valued for their warm sound, but its like a Rolls Royce - its still a car and you pay for the name. DPA condensors are well known for their clarity of sound, and are often used in classical recordings.
Those two mics (a dynamic and a multipattern condensor) will let you record vocals, most instruments and even get a decent sound from a drum kit (use the dynamic mic pointed at kit, and the condensor in figure 8 mode pointing left and right, and then look up "mid side recording" on the internet to find out what to do next).
After that, it up to you, and what you want to record. A matched pair of small condensors, an omni mic, a specialist kick drum dynamic, another large condensor with a different sound (if one sounds bright and crystally, try to get one that sounds dark and brooding - yes, they do exist in those extremes!), or even a ribbon (Royer, RCA, AEA all make good ribbons). Remember, no one mic does everything, so what you need is a collection of mics with different abilities - in terms of pattern and sound - so you have a good mic on hand for any need.
 A FINAL WORD
Even mics of the same pattern and mechanism can sound quite different. Before you buy, it is really worth getting to know the mics you already have, and try out a few borrowed from your mate or at your friendly local music store. If you know the brand and model of a mic that you know will give you the sound you want, you'll find your eBay shopping much more directed, with less mics discarded or left lying around.
Good Luck, and may you bid successfully!