@Alyssa, hey thank for your comment. You reminded me to play the game, fill in the blanks which I'm learning Frozen, Let it go. Also, thanks for your other suggestions. Have a good day.

Have you checked out Lyricstraining.com? http://lyricstraining.com/ I've used it for French and it can be addicting. It's an online game where you have music videos (or just lyrics) on the screen, then you need to fill in the blanks. It's great for listening skills.

For a catchy tune that everyone seems to know, I would check out "Party in the USA" by Miley Cyrus. It has some good informal English phrases like "to jump in a cab" "to have butterflies" (to be nervous) and "to hop off a plane", but not too many cultural or poetic references. 

http://www.azlyrics.com/lyrics/mileycyrus/partyintheusa.html

With song's lyrics it's almost unavoidable to come across metaphors and poetic license, slang or other uncommon uses of language. It's even possible to find out there are either intentional or unintentional errors or poor language use so you have to be careful.

If you're not interested in this kind of language use, maybe lyrics are not the best idea.

But if you are interested in that, then go for the genre you like. You have to listen to something you personally like. If you don't, you'll give up on it sooner or latter.

I personally like musical comedy so my favourite bands and singers are Tripod, Axis of awesome, Tim Minchin, Dead cat bounce, Nick Helm, Jon Lajoie, Bo Burnham, ...

Though some of their songs are not older than five years, I doubt this will help you in any way. 

Thanks for your comment! I'll look into it!