There are two basic types of microphone for home-studio & general use:

Dynamic microphones
These require no power from either an external power-supply or battery, and tend to be more robust and less sensitive than Condenser-type mics. Classic "Dynamic microphones" would be products such as the Shure SM57 & SM58, the Sennheiser MD421, the Electro-Voice RE-20 etc

Interestingly, here's a video comparing 3 of the dynamic mics that I mention; the Sure SM57, the Sennheiser MD421 and the Electro-Voice RE-20... it makes interesting listening.

The 3 mics are priced quite differently with the SM57 being around 90-100 euros, the MD-421 taking the center-ground price at about 260 euros, and the RE-20 bringing in the top price at around 460 quid!... as I say, it makes interesting listening... the SM57 is an under-rated vocal mic.


Condenser microphones
Available in different types, these mics generally require power of some type from either an external power-supply or from battery (or both in some cases such as with the classic AKG C1000s). Condenser microphones tend to be more sensitive due to the finer diaphragm, and thus are generally used where greater detail is required.