I am very new to using ubuntu servers and I have two of them. One has everything I need configured properly and working (it runs a nodes app that I developed), the other is a fresh, stronger server I just received. How would I go about copying/replicating the entire server from my first one to my second one? both are running versions 16.04
The are two things to consider: The installed packages and the configuration of those.
For the configuration, that's what configuration management systems are for. With just two servers it might look like overkill, but I would recommend it anyway, especially if you see a future with a third/fourth/... server. If you don't want a configuration management system, you'll basically have to copy the configuration manually.
For the installed packages: I don't know if ubuntu has some fancy tools for this, but ubuntu is based on Debian which does:
dpkg --get-selections >file dpkg --set-selections <file apt-get dselect-upgrade
Remember to read the documentation of any command before executing it, I would also recommend looking into the