>> keeps resetting itself to 255.255.255.255
That is the "broadcast" IP-address.
Compare to a person in a swimming pool having difficulty -- they broadcast "help help help" to every nearby person, hoping one person will rescue them.
Broadcasting a DHCP-request should be "heard" by some DHCP-server. The DHCP-server will respond to give a valid IP-address.
Any IP-address ending with ".1" is likely to be a third-party router, or a cable-modem, that is also a DHCP-server. That "1.1" response tells your computer that any IP-address NOT starting with "192.168.1" is NOT an IP-address within your home network, and that any packet you send must be "forwarded" to the router for the router to "forward" the packet out to the Internet.
On your computer, disable the "IPv6" setting for your network-adapter, so as to NEVER request an IPv6 ID to be sent to your computer.
Will that stop my router giving out a public facing IPv6 address? Will it stop me acessing IPv6 addresses on the Internet?
Or is it just related to private addressing, I'm assuming you mean disable it in the config properties for just the ethernet adapter on the computer