You will want the Wi-Fi configured as an access point or what Apple called "bridged"—this makes the Wi-Fi and wired networks appear connected and this with the appearance of no intervening IP router–or you will want to use an IP subnet for Wi-Fi and a second IP subnet for the wired network and with an IP router connected between those and with DHCP services provided by some box on each subnet.
If you want to run your own services on your network, not the least of which is DHCP services, and want a network that can have a couple of different Wi-Fi APs connected and active for better coverage—configuring each of your Wi-Fi boxes as an AP works well. This because an AP may or may not provide DHCP or other services.
If you choose to have a router between the networks, you will have to control what traffic traverses the router. You probably don't want it running as a firewall, for instance. Some network protocols and related network traffic such as mDNS are not (or are not, by default) passed through an intervening router. Whether and how a router can pass that traffic varies. Check the vendor docs.
Generally, you want exactly one box on your network providing NAT, and that is the box at the edge of your network, adjacent to your ISP. No other boxes within your network should be performing NAT. (This absent very unusual circumstances.)
I mostly run a mix of ZYXEL, Ubiquiti, and Synology gear on the networks that I'm managing, and some network services from Mac systems in certain cases. What D-Link and NETGEAR boxes had been around have all been retired.