Hej Amanda!
I've been learning Swedish for 18 months and would definitely recommend listening to as much Swedish as possible. In my opinion, listening is the most difficult aspect of Swedish, because people don't always pronounce things the way they're written (e.g. "Hur mår du" is actually pronounced "Hu må ru"). When I travelled to Sweden last summer, I found out that I could read, write and speak really well, to the point where I didn't need English at all... but I was incapable of understanding spoken Swedish. Today I'm much better but I'm afraid that my listening is still much worse than other skills. I would definitely recommend listening to Swedish as much as possible to get your ears used to the sounds of the language.
Look for a podcast called "Radio Sweden på lätt svenska." It's the news in easy Swedish. You can find transcriptions in their website if you don't understand something. It's great for practicing listening and after a month or two studying Swedish you should be able to understand what the podcasts say.
As for music, I'd really recommend Melissa Horn and Nordman. Their lyrics are not very difficult and their pronunciation is clear.
Good luck! :-)