Ethernet from modem to switch will not work. This is because every device connected to a network must have an IP address assigned to it, either a public one (for devices connected directly to the Internet) or a private local address. You can think of an IP address as sort of like a phone number. There are public phone numbers reachable from the outside, and there are private exchanges with extension phone numbers that work only within the building. The modem will get an IP address from your service provider. Whatever device you connect to the modem will get an address from the service provider through the modem. Most service accounts provide ONE address for ONE device (computer, TV, router, etc.). To get more, you have to pay more.
A router will use the public internet address given it by the modem and most can also assign local addresses to one or more devices. It then "routes" messages from your local devices to the various services on the internet and routes the responses back to the devices that sent them. Most routers provide Ethernet connections for multiple devices, but if you need more, a switch will do the job.
In addition, devices connected directly to the Internet are exposed to all sorts of attacks from nefarious people. One of the things a router can do is to help you protect local devices from some of these attacks. For more elaborate protections, you need more sophisticated infrastructure devices (firewalls) but that is beyond the scope of this note.
Hope i've explained things clearly enough.