Cat6 should do the job and I will also share something that improved the SQ in my system.
I had 2 Ethernet switches between my router and streamer and was running low $ Best Buy cables. I got an entry level Ethernet cable from Audioquest and eliminated both switches by placing a home run from the router directly to my streamer. I was careful to buy exactly the cable length I needed so there was no excess. I'm guessing that the improvement came from eliminating noise from the switches and perhaps, to a lesser degree, better shielding from the higher cost cable. The improvement in SQ that I most noticed was better detail in the soundstage.
Good Luck!