There are many different types of microphones. Dynamix, Condenser, Robbon, etc. I will give an example of an artist that I would recommend a vocal mic to. Pretend the artist is a rap artist with a budget of only $200. For this price range and genre of music I would recommend a studio condenser microphone.
Now you have to do research, either on the net or in person. Narrow down all of the mics in your price range and the same type as you decided on in the last step. Go to google and search for stores that sell various brands of microphones. Find the store that offers the most mics. Get all of there names.
Go online or to your local music store and get reviews of every mic you have on your list. Take reviews more seriously if they are in the same genre of music as you. Now that you have some good reviews on each of the products, you can begin to narrow down your list.
Now get on google and type in searches such as Microphone 1 vs. Microphone 2. This will send you to music forums and review sites that are comparing the mics. This will help you narrow it down to at most 2 mics, hopefully just one.
Now you have to research microphone preamplifiers, but that’s a whole other research process. You might even have to buy stuff like soundcards, audio interafces, mic stands, music stands, or any other product that a musician needs. Good luck in your music career.