I want to upload one of my songs but I don't' want others to be able to download

First complete the metadata on your song to include your name and the date you created it. You should be able to do that in your DAW, if not Google it, there are loads of free stuff you can download.
When you upload your song here on bandAMP there is a drop down menu giving three options on who can download the song. I think the one you want is www so that no one can download it. I've no idea why it's called that, but just try it and when its uploaded check to see if it can be downloaded when you call up the song, which will be listed on the home page and your home page under the music tab. If you are still not happy, simply delete the song from your home page music tab.
Anyhow, it's quite normal at first to be concerned of someone steeling your song, but the fact you have uploaded it here in the first place shows the date anyway and who created it.
Hope this helps

Here it is said: http://about.bandamp.com/rules.html

Chose "No" for your uploaded song and it cant be downloaded by anyone.
"Members" is just for members only to download
"WWW" is download for everyone from the web