An excellent guide on how to most efficiently search Spotify’s large music catalog.  

Of particular interest: you can search by genre, and the list of genres is quite extensive.  Spotify really should expose this capability better in their UI, but until they do so searching with the “genre:” prefix will have to do.   A list of genres for the US can be found here.

You can also search by label, or by a combination of criteria.  Read the full article for all the possibilities.