It won't register until you connect the Enet cable then direct the browser to
https://autoreg.autoregister.net ON THE PC THAT WILL USE THE SERVICE. More info here.
http://www.cableforum.co.uk/board/article.php?a=13
As for routers you need one that does NOT include an ADSL modem as these have an RJ11 socket for a phone not the larger RJ45 Ethernet port. As far as cabling goes Patch is recommended but some modems can use crossover, I do.
Belkin, Linksys and Netgear's 54g/802.11g "Cable Gateway Routers" are the recommended ones. I have a Belkin which is fine and the Linksys/Netgear get decent commendations from other members too.
They come with setup guides so it's a case of following them, from personal experience the Belkin is extremely facile but
DON'T FORGET TO SECURE IT!