Setting up music on an iPhone?

Hi, I just recently got an iPhone 5c, and was planning on downloading my music from the cloud onto it. Whenever I click on music, it lists all songs I, or someone else, have bought from iTunes. All of the songs aren't downloaded, but are just listed there. I want to just add my collection of music and get rid of the songs I don't listen to (and the playlists that came with the Phone, like 90s music or top played), but I don't know how.

Is there a way to delete all of those things off my phone?

Well, not off of your phone, but if you have a computer that has itunes downloaded onto it, I'm pretty sure that you can go into itunes and delete them there. But, otherwise I'm out of ideas.
I don't have any apple product, but my sister does, so I usually try to figure it out.

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