If I am understanding your setup correctly, the static ip's should just need to be on the same network id as the router. Find out what the ip of the router is. Router documentation should say what the default ip is. If not, the simplest way would be go to a command prompt and type in "ipconfig"

The default gateway address is your router. In most cases, you should have a 192.168.x.x address, if not, specify what it is. The first 3 sections of the ip will be the network id, make sure that those numbers on your static ip's match the numbers on the router. For example if the default gateway is 192.168.1.1, then make sure the static ip addresses are 192.168.1.x Then assign x a static value(between 2-254). If the other 3 get their address through dhcp, make sure the static addresses are outside of the dhcp pool.

I have a client with a similar setup. They have a Comcast Router with a fixed IP assigned with roughly 199 ip address available in the range. There are 8 desktop client machines, 1 wireless router and 1 network printer/fax connected to the router through an unmanaged 20 port Dlink switch. There is no server machine (all their work is remote via the internet). I have all the client machines setup to obtain IP and DNS automatically. There's been a recurring problem where internet service drops and when it drops, it effects all machines on the network, and (of course) Comcast is helpless to explain why but has replaced the modem and states there has been a history of loss of signal to the gateway. Would I be best to set each client with fixed IP and DSN settings? If so, what about the wireless router and the network printer?

not sure what digital printer you have however connecting the printer to a router could work and assigning dhcp to the desktop computers.