mac – How can I copy files on HD to external HD in recovery mode?

I’m having problems with my 2015 Mac and need some help.

Last night I tried to install a newer OS (Mojave) and it told me there was a disk management error (69854). I was previously on OS High Sierra.

I followed all the troubleshooting guides etc. and eventually had to
resinstall the OS in recovery mode. It took me all the way back to OS X.

Unfortunately I don’t have a time machine backup. OS X is installed but it won’t let me go past the login page. When I try to enter my password the screen refreshes and nothing happens.

I have decided that I want to invest in a new Mac. My question (unless someone can help me log back in!) is how can I copy the contents of my HD (all the files appear to be there still) onto an external HD?

I have read things about creating a “blank image disk” but I don’t know what the means. I’m inexperienced with this sort of stuff so any easy to follow help would be appreciated.

By the way, in terms of logging back in, I’ve repaired the “disc permissions” in disk utility but it’s done nothing.