Lots of people use Shure SM58 dynamic microphones and are happy with the results but for really clear detailed recordings a condenser microphone such as those made by Rode,Studio Projects,Red5 audio,AKG etc is much better but they are not so robust as dynamic mikes they also need external power either from a mixers phantom power or a separate power supply(usually but not always included).
There is also a type of condenser called a back electret which are usually cheaper than a true condenser mike but they are very good sounding the cheapo mikes that come with computer soundcards etc are also back electret designs but they use a heavier back plate joined to the mike diaphragm(the part that picks up the vibrations of the voice or instrument)which inhibits their ability to respond quickly to vibrations so they generally sound muffled.
A good quality back electret e.g. AKG C1000 apart from being cheaper has the backplate separate from the diaphragm which is suspended above the backplate,this type is very clear sounding,as good as a true condenser in many cases but has the disadvantage that after maybe 10 to 15 years the back plate loses its electrical charge and the mike becomes more noisy because of it.
If I was starting out with recording on computer and wanted good results for as cheap as possible I'd go for a back electret condenser(Stage line is a company who do cheap and good sounding back electrets)and a reasonable quality soundcard like the audiophile 2496 which is a 24 bit sound card with very good sound quality these 2 items will probably set you back between 350-500 dollars depending on where you shop.How may tracks you will be able to play back on your computer will be limited by how fast your hard disk is(at least 7200rpm is preferable).