It is unlikely that you will need to know all of this, but these composers should be useful for the common question "Name a suitable composer for this piece"
AOS2 -Shared Music
Possible composers for a...
Lied (Romantic Song) - Beethoven, Schubert, Chopin and Wagner
Pop ballad - Bob Dylan, Kate Bush, Sting, Elton John etc.
Classical Concerto - Haydn, Mozart and Beethoven
Jazz piece - Louis Armstrong, Duke Ellington and Glenn Miller (however, jazz is mainly improvised)
Classic Choral piece - Handel and…