well, if you want to get into the older stuff like shakespeare I would suggest just diving in. At first, just lookup the words you dont know and after maybe one play you should have already learned enough to understand his style and language and "get" his works on their face value.
as far as literary references go - aka john milton - (basically the only reason you'd need a class), I really think you'd just have to read/know most of the greek/roman classics and the bible to be able to get most of them. But no worries, if you enjoy reading the classics are a blast, the hebrew old testament is packed with pretty cool stories (the mad king Nebuchadnezzer) and it doesn't get much better than the iliad and odyssey.
as far as literary references go - aka john milton - (basically the only reason you'd need a class), I really think you'd just have to read/know most of the greek/roman classics and the bible to be able to get most of them. But no worries, if you enjoy reading the classics are a blast, the hebrew old testament is packed with pretty cool stories (the mad king Nebuchadnezzer) and it doesn't get much better than the iliad and odyssey.