Download previous itunes purchases?

my itunes account is shared between three different computers (a desktop and two laptops), and sometimes my family downloads songs that I want, but if I want them on my own itunes, I need to repurchase the songs. so you can imagine how awesome it was for me when I discovered that I could download previous purchases onto my own computer. but after I downloaded several songs, but after a dozen, a window popped up asking if I wanted to back up my purchases. Does this mean that downloading previous purchases cost money? and if it does, is there another way to access previous purchases that aren't on my computer on my own?