Virgin provide both *CABLE* and *ADSL* broadband, so the type of router depends on which broadband you have.
With "Cable", you use a "Cable/DSL" router whose WAN port connects by ethernet cable to the Modem's ethernet port.
With "ADSL", you replace the existing USB Modem with a combined "Router & ADSL Modem".
To print "wirelessly", you would either install a Wireless Print Server with a USB port for the printer to connect with or, as you're to be using a wireless router anyway, you could connect a "wired" Print Server to the router. As the computers are connecting "wirelessly" to the router, you can still print "wirelessly".
Because wireless networking runs over "radio" links not, for example, Infrared you don't need a direct line of sight between components.