In the Web-based UI (which it looks like you already know how to access), at least some of the settings are likely to be under Firewall > IP Passthrough, and if you choose to do this you’ll also want to disable the gateway’s radios, as @dave27 indicated, which should be at Home Network > Wi-Fi > Advanced Options, as you’ve shown. I don’t know which particular gateway you have, because the UI in your screenshot doesn’t look exactly like what I see on my gateway, but you should be able to plug the model number (i.e., BGW210 or whatever) plus passthrough into a search engine to find instructions that others have written. I haven’t ever done this (haven’t had a particular need), so I can’t comment on the reliability or accuracy of those instructions or recommend a particular guide.
I saw your mention of a doorbell in another topic you started, but I don’t recall seeing any mention of a particular model, so I don’t know if that factors into your experience here.
If you’re using IP passthrough and disabling the gateway’s Wi-Fi, then Ethernet is really your only remaining option to connect to the gateway. You’d connect a cable from one of the gateway’s Ethernet ports to a port on the router (probably the WAN port, depending on the router).
Others here in the community will be able to give much better advice than I can regarding router selection. I’ve had satisfactory performance so far (especially since the fiber upgrade several months ago) with the ISP gateway plus an additional wireless access point, so I haven’t bothered with a router upgrade. I’m not knocking that as an option; I just haven’t had the need and have had other priorities.