Is it a wireless router or a cabled one? It doesn't really matter anyways, just wireless allow easy access to computers further away from the access point than having to route CAT5 cables all over the house
Most new Linksys routers have 4 ports so this is going to work perfect for you. If you want wireless setup, you need to get LInksys wireless cards for all the PC you wish to be added on to the network. YOu can have at least one wired one. That is the one that is directly connected to the printer. At least, that is how I configured mine. The others can all be wireless.
When you plug everything together, you should automatically have internet access to all PCs.
To enable print sharing, you have go into My Network Places and select Setup a small home or office network on the left side of the window. Go through the wizard. Do this for each computer you are networking to the printer. This will also enable file sharing automatically too. It's a lot of fun to do and having a network increases productivity by doing less work.
After file and print sharing is enabled, then you need to "Add new printer" from the print folder. You will be using a network printer this time, not a local printer. Follow the wizard again. It will scan the network for a printer and will find your all in one printer for you automatically to install. Do this for each PC too. That's it.
After all that, you can configure router security too. Make sure your firewall accepts the IP and'or MAC address for each PC, other wise, no network activity.