I am posting this in case anyone else has trouble installing/running the browser on a fresh installation of Ubuntu 18.
After downloading the SAFE Browser zip file for Linux, double clicking the safe-browser icon didn’t start the application. I tried to open the application from the command line, but I got this error message:
./safe-browser: error while loading shared libraries: libgconf-2.so.4: cannot open shared object file: No such file or directory
It was apparent that I needed to install that package to get the browser to run.
sudo apt install libgconf-2-4
Then I was able to launch the browser and register my account!