All people in the recording should use a computer (not a phone) and headphones with a mic. More recording tips attached from our friends at ArtLab Chicago (they're available for recording support!).
Rehearse: Set up your microphone, call someone, and practice recording and downloading a conversation. Then view the recording and troubleshoot any unexpected issues.
Record the meeting and save it to the cloud. That tends to be more reliable, and doesn't fail if your computer can't handle video streaming.
30 - 90 minutes after the recording, it will be done processing. Download the final video.
You may have a limited space in your Zoom account, so try to download the Zoom mp4 files soon after the recording, relabel them, do any editing you want to do, and back them up (and/or upload them to YouTube) shortly after the recording in case you need to start deleting recordings from your Zoom account.
If you want the videos to be public, upload them to Youtube. If you want to hide them from the general public, set it as an unlisted YouTube video.
Let us know how it goes!