The modem is not also a router. So it has to be on the router's WAN side.
The modem, not being a router, will only supply internet access to one device, that has to be the router.
So the computer will need to go through the router to get to the Internet. But that's precisely what you wanted to avoid by using the switch.
So this leaves two options:
Use the computer as a router and use the router only as an access point.
Accept that only the computer will have internet access and no other devices will.
Either way, you'll have to configure two separate networks that run over the very same physical network.
You can simply assign the computer IP address 192.168.0.1/24 on this network, assign the router 192.168.0.2/24 and the printer 192.168.0.2/24. You can't use DHCP to autoconfigure. So you will have to figure out how to assign the printer a static IP address.
You will have to figure out how to get the computer to get a dynamic IP address from the modem for the WAN side but also use a static IP address on the LAN side.
Ideally, the computer would have two ethernet ports, one for the modem and one for the switch. Then your WAN and LAN networks could stay physically separate.
This is a complex and fragile configuration that requires some expertise to configure, understand, and maintain. Using a switch with VLAN support would simplify it. Personally, I'd suggest just getting a decent wireless router with gigabit ports. Something like the Belkin AC1600 is around $40.