Yes, you can do this all through any router. The traffic is all TCP/IP, so it doesn't matter who made the box, just as long as it handles it properly-which just about any consumer-level router should do just fine. Linksys routers WILL do fine with this; I have one handling my network right now.
You may find some issues with sharing a USB-connected printer. Not all manufacturers write their drivers so that they share well. My Brother HL-2040 has both parallel and serial ports, so I connected it to a parallel print server on my network. It shares fine this way.