Wired network adapter

Hello :)

So im finishing up this build of mine, what i want to do is use my wired internet connection from router, to my older pc which i would like to use as a small server for stuff like day z and Arma 3 missions, then if its possible wire from my old pc to my new build. If this is nonsence please let me know, rather it would be easier just wiring each computer with the router separately. But id it is possible please let me know what i would for this.

I am using this mother board on my new pc: http://www.newegg.ca/Product/Product.aspx?Item=N82E16813131877

Also would this do and also work in my MoBo: http://www.newegg.ca/Product/Product.aspx?Item=N82E16833166096

thanks so much for any help

it's called a network bridge.

hook up old pc to new pc, new pc to router, go into new pc network devices, highlight both of them, right click, bridge connections.