I have an ethernet port that I want to turn into multiple ports
You are probably looking for a switch or a router, but not for a DSL router. If your Verizon coax modem already works like a router, you do not probably need another router, just buy a switch.
Routers connect two or more logical subnets, which do not necessarily map one-to-one to the physical interfaces of the router.
If you do not need to create two separate networks with different network rules (like firewall rules), you do not need more than 1 router at your home. Nowadays most modems come with functionality of router so that you do not need to configure both router and modem as two physical devices.