You didn't try the by far most popular option - OBS Studio.

To get the best audio results:

• add proper source for your input device, e.g. microphone
• add filters to the created source to process the audio on the fly, e.g. remove noise, add some gain and limit max dB treshold. There are lots of videos on e.g. YouTube explaining how to properly set up filters.
• add any other sources for whatever you want to record, specific windows are recommended. If you need other sound from e.g. the system, using Application Audio Capture source is recoomended for the best control.

A simple one is simplescreenrecorder which can be found in the 18.04 repo. Install it with

sudo apt install simplescreenrecorder

start it > Continue > choose size of screen to record > tick the box for audio. For Backend choose pulseaudio. For source choose built in audio analogue stereo which would record the mic instead of the internal audio > choose save location and the default codec parameters should be ok

SimpleScreenRecorder (source code) did the trick for me when recording online playing videos. It has an (experimental) OpenGL feature. On Ubuntu:

sudo apt update
sudo apt install simplescreenrecorder

With the OpenGL feature you can select to record a specific application window. So you can even keep working while recording in the background. Don't play any music though, because the audios will mix together (unless, of course, you are a DJ ;) )

gtk-recordmydesktop

Adds an easy to use graphical icon on the GNOME toolbar to make a pleasure use and configure the audio and video capture and screencast application recordMyDesktop.

As mentioned at 20.04: Can't install gtk-recordmydesktop and on the package search, the package is not available on the main repository anymore, and sudo apt install gtk-recordmydesktop fails. I'm not sure why the http://apt.ubuntu.com/p/gtk-recordmydesktop link seems to work, maybe it installs an older version. But this indicates that the software is not being actively supported.

recordmydesktop

This is the non-GUI backend of recordmydesktop, and it is still available in 20.04:

sudo apt install recordmydesktop
recordmydesktop --on-the-fly-encoding

This will record until you stop the program on the terminal e.g. with Ctrl + C.

--on-the-fly-encoding encodes the output immediately; without it you need to wait for a possibly long time at the end for the encoding to be done. I haven't seen any significant downsides to that option yet, likely it will just take a bit more of CPU resources, but it is generally worth it.

It should be able to do everything that gtk-recordmydesktop does, but it is a bit harder to learn as you have to deal with the command lines.

You can set a stop recording shortcut e.g. with:

recordmydesktop --stop-shortcut=Control+s

You can select to record a single window as shown at: How can I get the value of Window ID?

recordmydesktop --windowid `xwininfo | grep 'id: 0x' | grep -Eo '0x[a-z0-9]+'`

This will allow you to first select the window with a mouse click, and it starts recording after you click.

How to record sound output with it: https://unix.stackexchange.com/questions/3490/how-can-i-record-the-sound-output-with-gtk-recordmydesktop

xvidcap (no longer maintained, package is no longer available)

A screen capture enabling you to capture videos off your X-Window desktop for illustration or documentation purposes. It is intended to be a standards-based alternative to tools like Lotus ScreenCam.

Video can be saved in MPEG or AVI files format.