I figured I could have a page like this since most people do that on here. Not to mention, my music taste is kinda old-fashioned, so I figure that the large majority of the userbase here will have no idea what any of this is. That being said, I'll be sure to describe the genre a little bit before listing my favorite artists.
Instrumental
Ragtime:
Ragtime was formed in African American communities within the southern United States during the late 1800s and popularized in the early 20th century. This is the first uniquely American genre of music. It is rather iconic and has a very distinguishable sound, combining classical music and syncopation. It's very popular in modern video games, and had quite the influence on genres that came after it, including jazz, swing, stride, etc. If you don't care to check it out, just think of silent films, saloons, and circus music.
Boogie and Blues:
Blues music was developed during the mid-1800s deep in the Southern US within African American communities. Blues as a genre is really quite vague, so just understand what a blue note is and that's pretty much all you need to know right now. Boogie Woogie is a subgenre of blues music popularized during the 1920s, though it was being developed in African American communities long before then. It is characterized with its consistent bass line, which is usually a 12 bar blues, though 8 bar blues isn't uncommon. Blues, and boogie woogie especially, had a large influence on R&B music and later Rock 'n' Roll music.
Vocal
Barbershop:
Modern barbershop music was developed during the 1930s, with its exact origins being somewhat debated. It's an a cappella style of music, defined by the Barbershop Harmony Society as, "...a style of unaccompanied vocal music characterized by consonant four-part chords for every melody note in a primarily homorhythmic (the same word sounds at the same time) texture." While typically thought of as being performed by quartets, it can be performed by choirs as well, and often is.
Rock 'n' Roll:
Rock & Roll is not Rock music. Rock 'n' Roll specifically refers to the style of music developed in America during the '50s, which later evolved to the more international and vague genre of Rock. It drew from the previously mentioned genres, as well as gospel and country. Piano or Saxophone was usually the lead instrument, later being supplemented or replaced entirely by guitar.