The Kindle really needs to connect to the internet using WiFi.
I have Virgin 10Mbps Cable and use a D-Link DIR-615 which I believe is the model Virgin supply (or did supply) although I bought mine myself. Any wireless "Cable/DSL" router will be fine, just be sure *NOT* to get an ADSL Modem/Router. Cable routers don't incorporate a modem and connect by ethernet cable to Virgin's Cable Modem.
I have the Kindle software installed in the PC and use that to buy and download books. I then start the Kindle, which synchronises with Amazon, and download the same book to it, via a direct WiFi connection to the router.