How to pick an IP

I'm planning on demonstrating a project that uses WiFi to control a device connected to a Uno R4. I would like to choose an IP that I can use for the Uno R4 acting as a server.
I plan to also have another Arduino, Raspberry Pi Pico, acting as a client. Again I must choose an IP.
Where I am going, there is a local network that talks to the Internet. I have no access to it. I want my devices to be completely independent of it.
Should I use an IP that starts 169.254? Can I arbitrarily assign the last two numbers?

Try hosting server using Access Point and connect devices to it

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Start with the UNOR4 WiFI example 'AP_SimpleWebServer'.
It will create a soft Access Point where you can set the IP address. The sketch setting a network with SSID 'testAP' and passphrase 123456789.
Now you need to connect to the testAP network and then connect the browser to 192.168.4.1 (or different IP if you changed). Attached is a client example for on another ESP32 board to connect to testAP and switch the led.
WiFiClient_Led_AP.ino (3.3 KB)

I think I was confusing things in my original post. Now I think that my access point can use any IP as long as there is no other access point within WiFi range that has the same name, password and IP. If two people within WiFi range were to implement the example code without changing name, there could be a problem.

BTW, I think that "Access Point" in this context means the same thing as "Ad hoc network" in some other documentation. Is that true?