I have a Zyxel NBG6515 Ac750 router and i´ll get buffering on 4k material. Should I get faster router and what would be recommended? Or should I just plug it with gigabit ethernet cable? I am using Nvidia shield as my device.
If shield has an ethernet interface, I recommend you connect it to one of the gigabit interfaces of your router and your TVs to the 5Ghz network provided by the router.
Do not use 2.4ghz.
Should CAT6 cable be sufficient?
Yes. Cat5e works as well.