Ok, want to download music.

I have an iPhone, but would like to be able to download music, so that I can workout, walk, etc. I am having trouble finding something that is working with my phone. As hard as that sound, believe t or not. I really would like something where I can either just find a some that I like after listening to it, download it, keep it, find it from a list and down load it. So far all I can get it random radios. But nothing that will stay on my phone. I just want, the same songs I downloaded to go back to...

Thanks
Jessica