For whatever reason, I need to run "systemctl restart network" after I login in order for everything to run smoothly. What do I need to do to automate this?

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As root, create the file /etc/rc.d/rc.local if it doesn't already exist, and put that command in it. A very simple form of the file might look like this:

#!/bin/bash

systemctl restart network

Then use chmod to make it executable, like this

chmod o+x /etc/rc.d/rc.local

Systemctl is supposed to activate rc-local.service whenever it finds that file, but it can't hurt to make sure:

systemctl enable rc-local.service

This will restart your network at the very end of boot but before you log in. As ILMostro points out, finding out why this is happening would be better, but at least this should make things easier until you do.