Well for one you don't need 2 different Ip addresses from your ISP. When you use a router you generally use a private address range(192.168.0.0-192.168.255.255 is class C private)and gives the devices on your network whatever IP you want to. Your "default gateway" will be the ip address assigned to the router. The router is in a sense the "gateway" to the WAN link(Internet).
As far as cables go, use the standard cat5e or cat6 ethernet straight-through cables.