How do I show memory usage information in top bar or as notification?

You may try a GNOME shell extension called "system-monitor". It does

Display system informations in gnome shell status bar, such as memory usage, cpu usage, network rates…

"system-monitor" depends on a few packages. To install them, run

sudo apt install gir1.2-gtop-2.0 gir1.2-networkmanager-1.0 gir1.2-clutter-1.0

Then log out and log in again.

As pointed out in the other post you want to install the Gnome Shell Extension system-monitor There's a browser plugin and integrations that can allow you to install it from the browser or from the software center as mentioned by @pomsky.

However I've found that the easiest way to install it is to just install it from apt using the debian package

sudo apt-get install gnome-shell-extension-system-monitor

This will also pull in all the required dependencies, and after a reboot or log out the system monitor was in the top task bar.

(Note that I think I enabled the swap manually before taking the screenshot.)

In Ubuntu 18.04 (assuming you're using the default gnome desktop at least) run the gnome Tweaks app. Everything you need to manage for that is there, including what exactly you'd like to see from gnome system-monitor on the dock bar, which you can configure through the settings icon near the on/off switch for system-monitor seen below.

Unfortunately the extension doesn't really fit the dock's default color so it might be a little ugly when you configure to see graphs and not digit values there. So I ended up configuring to show the digit value only for now.