Internet -> router/firewall -> your network with all devices
No DMZ needed or wanted.
You will want a dhcp server which will likely be the router/firewall. It will tell all your internal systems to use it as a “gateway” for Internet traffic. The router then allows outbound for everybody and does NAT - basically it makes requests on that systems behalf and sends the results back. If your want external access to a system you configure port-forwarding on the router (again it acts as the middleman between external and internal systems).
Edited to add: I love that you provided a diagram though! Makes it much easier to discuss.