Hi everybody. 
I managed to install FusionAuth on Ubuntu. Went by the official guides and ran
sh -c "curl -fsSL https://raw.githubusercontent.com/FusionAuth/fusionauth-install/master/install.sh | sh -s - -z"
Taken from https://fusionauth.io/download/.
This properly installed FusionAuth. After some fiddling around with the database setup, I can now run /var/lib/fusionauth/bin/startup.sh and FusionAuth will be up and running.
According to the documentation, services for systemd should have been installed, but that somehow didn't happen. So I can't call systemctl start fusionauth-app, also there is no file at /etc/init.d/fusionauth-app.
In order to still have FA running as a service, I created a quick systemd service configuration:
[Unit]
Description=FusionAuth
[Service]
Type=forking
ExecStart=/var/lib/fusionauth/bin/startup.sh
[Install]
WantedBy=multi-user.target
Sadly, this doesn't work. Does anyone have a working service definition or are there some templates?