uploading to cloud

A while ago I noticed a lot of my iTunes selections were listed double, one on the computer and one with the iCloud. I didn't have any second device and this doubling of songs bothered me so I deleted all the selections that had the iCloud icon and that were listed doubly in my iTunes.

NOW, I have my first iPhone. How do I get all iTunes store purchased music to go up to the cloud? I have an iCloud account that I can sign into. If I have all of my iTunes purchased music in the cloud will I have to have it show double if I also want a copy downloaded in my computer?

Thanks,

James