I love many kinds of music: country, rap, hip-hop, jazz, and rock.
A colon is used before a list. The best way to double check if a colon can be used or not is to get rid of the information after the colon. What's left should still be a complete sentence. Use this check for option 2 - "His paintings are of" is not a complete sentence because the preposition doesn't have an object. Option 3 doesn't have a verb so the entire sentence is completely wrong anyways. Option 4 "Certain footwear is required, namely" is also not a complete sentence. But our answer "I love many kinds of music" is a complete sentence before the colon.