Do I have to buy a router/switch or can I just use a switch?
Here’s how I understand it:
If I buy an 8-port switch, I can just connect the Ethernet cable from the antenna to one of the ports on the switch. Then I plug in all the other PCs to the other ports.
When a new PC is plugged in, it will just send a DHCP request to the antenna equipment (which I understand has DHCP services), and everyone will have an IP address provided by the antenna’s DHCP address pool.
That’s how I see it. Do you think it will work that way?
What else can you suggest?

1 connection, 1 computer, switch or no switch. To connect more computers you need a router.
If "the antenna equipment" has a DHCP server, then it’s a router, so you won’t need another router, just a switch. But if it’s your provider that’s providing the IP address with its DHCP server, you’re only getting 1 IP address, no matter how many computers request it.
Check the computer’s IP address to see if it’s drawing an internal address (10.0.0.0 – 10.255.255.255, 172.16.0.0 – 172.31.255.255 or 192.168.0.0 – 192.168.255.255) or an external address (anything outside that range). If it’s an external address you’re going to need a router.