Addendum: As mentioned I wanted to add a USB WiFI dongle so that I can move the RPi1 to my workbench, away from the Ethernet switch.

I bought a Mediatek MT7601u WiFi USB dongle from eBay. The Linux drivers are in-tree, one should ignore the link to the manufacturer drivers, those are years old. Even after entering the SSID and PSK using raspi-config I had problems activating it on my RPi1, not helped by the fact that it would disconnect the headless RPi from the network  when I plugged the dongle in. I tried the dongle on other machines and it worked fine though I noticed it ran fairly hot.

So I connected the RPi to a keyboard and monitor and noticed that the RPi rebooted when I pushed in the dongle. I had thought it disconnected from the Ethernet because it was reconfiguring the interfaces. It was actually rebooting. Long story short, the voltage from the power supply (an old repurposed power brick for a Zip drive) was drooping due to the current drawn. When I substituted a better power supply it worked fine.

Maybe the MT7601u is cheap and nasty. I don't know if newer dongles would draw less current. Anyway aren't you glad that modern microcomputers have built-in WiFi?