I have 3 iPod's running off my Mac - an iPod Photo, an iPod and an iPod Mini. They all co-exist quite happily. The paid for music should reside on the computer within iTunes - all the iPod does is sync itself to whatever you have in iTunes on the computer.

With the new iPod you should not need to run the CD that came with it as all this does it install iTunes on the computer (which you already have). You should be able to just plug the new iPod into the computer and let iTunes recognise the new iPod and take you through the necessary steps to set it up.