Back in the old days, if you connected 2 ports to 1 switch it would cause routing issues/network storms etc.
Modern switches should prevent that, but unless you have managed switches, and know how to configure link aggregation, just leave it as 1 per switch
Just get any switch that can handle 1000mbps - which should be all of them by now.
No switch performs better than another - that anyone would notice in the real world.
But if you want that warm, fuzzy feeling get one from a known manufacturer: netgear, tp link etc
One device, connected to another - like a router (via cable/Wi-Fi etc) is a network. And it’s at home so you have a home network.
Having extra switches, Wi-Fi extenders, access points, Ethernet cables etc are all just extras to make a bigger/better network to ensure all devices can connect for the best experience
That’s coax. Could be tv?