As tom as suggested I’d certainly start with your router and port forwarding. If you are sure that is setup correctly then you can setup the firewall rules.
I generally setup a /etc/firewalld/services/plexmediaserver.xml and add the following content to it…
<?xml version="1.0" encoding="utf-8"?>
<service>
<short>plexmediaserver</short>
<description>Ports required by plexmediaserver</description>
<port protocol="tcp" port="32400"></port>
<port protocol="udp" port="1900"></port>
<port protocol="udp" port="5353"></port>
<port protocol="tcp" port="8324"></port>
<port protocol="udp" port="32410"></port>
<port protocol="udp" port="32412"></port>
<port protocol="udp" port="32413"></port>
<port protocol="udp" port="32414"></port>
<port protocol="tcp" port="32469"></port>
</service>
Then run these commands to configure it …
sudo firewall-cmd --add-service=plexmediaserver --permanent
sudo firewall-cmd --reload
sudo firewall-cmd --list-all
That should configure your firewall correctly. At least it what I have been doing for years. Below are two useful links which I used when I was setting up my server…
One final comment, Ubuntu 16.04 LTS. You really want to run that old version ? Seems risky especially when you are opening ports and having it access the public internet.