Yeah this is definitely a big question for this particular theme.
I actually don't know enough about anything to make any recommendations. It suits my purpose in my specific case not to actually use the song itself, I think, or if I do, to use a recently released free version. My usual approach to these things is the "the people totally won't care" approach - i.e. make it and if someone is unhappy, discuss it with them, and if they demand it be taken down and so on, so be it.
I recently made a Seinfeld-themed game which ripped art and so on from the show and the only reaction from Seinfeld-land was that their official Facebook account wanted to post it. When I made a game of performance artist Marina Abramovic's performance, she just wanted to work together. And Epic Sax Guy never got in touch.
But I guess you still have to be willing not to share your masterpiece if the original creator isn't into it and notices...? I don't know - is this terrible advice/thinking? Someone else who actually knows anything?