For your requirements, a practical starting point is to use your Mac's built-in screen recorder and then edit the recording in iMovie.
Before recording, decide the dimensions you want for the finished video and keep the application or window you are demonstrating within that recording area. This helps maintain a consistent format across your tutorials.
Press Shift-Command-5, choose Record Selected Portion, and adjust the recording frame to the area you want to capture.
Under Options, select your microphone to record your narration.
You can also choose where the recording is saved and set a recording timer.
Apple’s current instructions are here: How to record the screen on Mac. In macOS Tahoe, the Screenshot toolbar also includes the option to record a selected window.
When you finish recording, click the Stop button in the menu bar or press Command-Control-Esc. The recording can then be opened in iMovie for editing.
In iMovie, you can trim the recording and add explanatory text directly over the video. Apple’s instructions are here: Add titles in iMovie on Mac.
You can also use iMovie's picture-in-picture overlay feature to place another visual element over the screen recording; this may be useful when adding a logo, depending on how you want the logo to appear. (Apple Support)
If you prefer to record and edit within one application, Screen Studio and ScreenFlow are alternatives you can investigate.
Before choosing either, verify that its current version supports your preferred recording dimensions, microphone recording, text overlays, logo overlays, and any other audio you need to capture.
One final point is to distinguish between your microphone narration and audio produced by applications on your Mac.
If your tutorial only requires your voice, selecting your microphone in the Screenshot options addresses that requirement. If you also need application or system audio, confirm the recording capabilities and setup required by the software you choose.
For your stated requirements, the overall workflow is therefore: choose your intended video dimensions, record a selected screen area with your narration, edit the recording, add text and your logo, and export the finished video.