Are you using wifi on the desktop or hard wiring it through an ethernet port? If the latter then you don't need any software on that PC as the operating system will negotiate with the router. Having one PC hardwired to the router will be an advantage should the wifi stop working, although plugging a laptop in is hardly a major inconvenience.
On wifi connected machines you will need to install drivers for the adapters in each machine. If these were factory fitted then they will already be equipped. The Linksys router wil come with a CD containing a utility to install on your machines. If you are using Windows XP then this utility is unnecessary as XP has all the software you need.
Lastly, enable encryption on your router to prevent neighbours using your bandwidth and accessing your files. Do this after you have got the system up & running and from a PC hardwired to the router.