lets start with the gateway (router) which connects to internet if i read correctly .... those devices have a built in switch and hopefully it is a gigabit switch ... though quality of those is usually not the best ...
basically you could add another switch on the end of the cable coming from your router - just consider now the traffic of 2 computers flows through a single port on your router, which might be a limitation of bandwidth ....
wherever possible i'd get some mid-range gigabit switch (say 8 port) connect all computers there (seperate cables) and use the router only as uplink to the internet resp. for the wireless client.
additionally: in a 100 mbit network there are tow different cables to be used
straight through (between router or switch and computer)
crossover (between router and switch or computer and computer)
gigabit is autodetecting so it wouldn't matte which cable you're connecting
never stack more than 2 switches in series (be it the built-in on thge router or a seperate one) - timing might become an issue ...
whenever possible try to restrict broadcast messages from a wireless router to the wireless part only - having those on the cable network can disturb reliability of connections (especially streaming)
hth, christian