You should read Greek mythology.
The last word would not be capitalized because mythology is not a proper noun. It also does not go hand-in-hand with Greek as some sort of compound noun. Greek is simply describing the type of mythology you should read.
It should also end in a period because you are being told to read something. They are not asking you a question, they are suggesting something to you. It is also not necessarily an exciting statement, meaning there would be no random exclamation mark at the end.
