I too would love to use at least some 10GBaseT connections, but the cost of doing so is prohibitive. And wouldn't do a bit of good for internet / streaming etc... Very few companies make 10GbaseT equipment, and those that do, know its value in an enterprise environment. None of them make or market anything in 10GBaseT that is priced toward residential installations, or even small to mid sized business applications.
For your configuration, I would suggest going with a quality router with gigabit LAN ports, and a 16 to 24 port unmanaged gigabit switch.
Since you don't mention any need for WiFi, or USB printer / storage service from the router, I would figure something similar to my rig would work well for you.
Router. Cisco / Linksys EA2700 4 port Gigabit LAN ports, gigabit WAN port, and 802.11n N600 WiFi.
Switch. TrendNet TEG-S16DG 16 port unmanaged gigabit ethernet switch. Unless of course you want all 16 cables connecting to the switch only, which is best, then you would want the TEG-S24DG 24 port unmanaged gigabit ethernet switch.
Both of those items cost less than the low end of a single port on a 10GBaseT switch... You will get, assuming your computers have gigabit NICs gigabit speed, unblocked (dedicated, full speed) all the way up to the uplink to the router, the router uplink would be shared gigabit, and the WAN port would be shared to at whatever speed your ISP provisions. Assuming you are willing to spend gobs of money, and it is available near you, a max of 302mb/s for residential service...