If you're on a recent version (Mojave+), you can press Command-Shift-5 anywhere to bring up the new screen capture overlay. The first 3 modes in the floating toolbar that appears near the bottom are for screenshots, and the following 2 are for screen recordings.
(This is the same UI that comes up now in QuickTime, but you don't have to launch the app to get to it.)
You'll also want to make sure you pick your desired mic input from the Options menu.
After you hit record, the stop button will appear in the menu bar on the right.
With your recording open in QuickTime, press command-t to trim the start and end.