Use of a lan hub/switch

Hello

I have a home computer network comprising of a cable modem (for the internet) which plugs into a Belkin Wired/wireless router. I want to drop a Cat 6 cable through the floor to hook up 3 PCs downstairs.

Am I correct is assuming that the cable that runs through the floor will need to be plugged into a network switch (http://www.dse.co.nz/cgi-bin/dse.storefront/4427cc330a34d5f2273fc0a87f99070f/Product/View/XH8258)

and then 3 more Cat 6 cables are plugged into the switch and to the 3 PCs?

And does it matter is I use a crossover Cat 6 between the router and the switch or must it be a non-cross over cat 6?

If someone could explain it all to me I would be very appreciative.

Many thanks
Confused – Bruce