Which sound profile will allow me to simultaneously hear and record system audio + microphone input?

Solution 1:

No sound profile selection will achieve the results you are looking for. Instead you could mix voice and audio channels (follow link for step-by-step details).

You might want start with this article from the same blog for background High quality audio broadcasting with Flipzu and Ubuntu Linux, or this "weekend project" for a lot more technical detail: Record From Skype Calls and Other Apps on Linux.

Solution 2:

install & use pavucontrol

sudo apt-get install pavucontrol

executable : /usr/bin/pavucontrol

this software monitor audio output and can map audio input to monitors.