There are two slightly different ways to do this. You are each talking about one of them.
One way (the way I would do it), would be to plug the linux box into the WAN port of the router. This is cjcox's method. Set the router's external IP address to something on the same subnet as the linux box's eth0, then set the router's gateway to point to your linux bridge (you probably would also need to enter your ISP's dns servers). Anything on the inside could then use DHCP easily.
The other way is to just do every thing on the LAN. Using the LAN ports, just set up everything as static. This is what KohlyKohl is doing. Point everything at the linux box instead of the router. In this setup, the router isn't routing, but is just acting as a switch (and wireless bridge).
The reason I would go for the first one is ease of adjustment and security. If I had more than 2 computers, or a friend brought over a labtop, I think it would be a little less hassle to add additional machines. Besides, if the internal machine is a MS Windows box, having NAT protection at the router would help keep some of the viruses out (the second solution doesn't use NAT, the first usually does, depends on the router). There are arguments to be made though, to not having them separated by NAT (file sharing gets trickier).