do I need to download operating system to play on computer

You can download iTunes for Windows or Mac from http://www.apple.com/downloads/ . Then you can use iTunes to reformat the iPod, if necessary, to get it to work with your system. iTunes is also the program you'll use to get music and media on and off of the iPod and control some of its settings.

An iPod that's only been used with Macs before will have to be reformatted to be usable on a Windows machine. Once iTunes detects such an incompatible iPod, it should automatically display a window giving you the option of reformatting it.