I have a linksys router that all of my computers are using, into a cable modem.
it should work fine, you don't need to open any ports unless you want to host a RW session (and possibly H2H?), or any other server. Tho that will also require you to use static IP's on your computers (can't use DHCP with port forwarding).
Anyhow, in the simplest case, you should just have to plug your modem and computers into your router, and dhcp will do the rest.