Chronologically, I tried this afte Solution #2 - in which I uninstalled amdgpu, but kept to using gdm3 and gnome.
Then I downlaoded amdgpu 18.30 driver and installed it. It needed two reboots, but now it seems to be working fine.
Uninstall amdgpu driver.
After restart, I was presented with gdm3 and could successfully log into my desktop.
The solution with installing lightdm got me only as far as seeing lightdm, but gnome still couldn't load and crashed.
+1: I only accepted the online update. I was already using 18.04 from a fresh start.
I could start the recovery mode.
Going to full mode from recovery mode gives access to some extra info. From the logs I see that gdm starts but then hangs:
Started Session c4 of user Gdm.
Starting User Manager for UID 120.
Started User Manager for UID 120.
Starting Manage, Install and Generate Color Profiles...
« and there it hangs, the screen is flashing from console to graphical purple and back then it all stops.
Updating gnome-core by hand didn't help.
Not sure it is relevant, but in the journalctl -k:
[drm:amdgpu_init [amdgpu]] *ERROR* VGACON disables amdgpu kernel modesetting
[drm:radeon_init [radeon]] *ERROR* No UMS support...
There is "blacklist radeon" in my /etc/modprobe.d/blacklist.conf.
The solution above got me to a login screen, but I cannot actually log in (gnome crashes) and ctrl-alf-f* to another console crashes too, not even letting me to a shell.