The advantage of using a dynamic microphone is that besides it's inexpensive, it's also less sensitive to background noise. The speaker needs to speak or sing at a distance pretty close to the mic. No need of a 48V phantom power provided.
However, dynamic mic has its disadvantages. Human ears can hear sound frequencies ranging from 50Hz to 20KHz. Dyanmic mic usually respond to frequencies below 16KHz. The loss of certain ambience frequecies make the recorded sound a bit unnatural, dead and not so pleasant for vocal or song recordings. That's why for studio vocal recording use, most likely condenser mics are used.
Yet, if your requirement is not very high, the dynamic mic like Shure SM58 can be a very good entry level recording mic. When you're more comfortable with the setup, more skillful in working on sound projects, very likely you'll use a condenser mic.
To choose a mic, besides the type, its polar pattern and frequency response charts are 2 very important specification that every sound engineer will read. The polar pattern basically tells you how your mic responds to different frequencies of sound when the sound source is at a different angle. Usually, the most sensitive point is right in front of the mic (at zero degree). The frequency response chart tells you how a mic responds to different frequencies of sound, as well as the range of frequencies it covers.
This is an example from Shure SM58 dynamic mic: