If your devices only support up to 4K at 60Hz, a "premium high-speed" HDMI cable (18Gbps, HDMI 2.0) is perfectly fine. Again, just avoid really old or thin cables. Early HDMI cables (HDMI 1.4 or older ...
Even fast internet slows when dozens of devices compete for bandwidth. A VLAN setup separates traffic, reduces congestion, ...