Which volume or container should I select if I want to run Disk Utility's "First Aid" simply to check my computer's well-being?

Glad you asked because this has been Everything You Always Wanted to Know About DFA* (*But Were Afraid to Ask) for me lately.

I have used Disk First Aid via Recovery mode and checked all items from top-to-bottom (i.e. device-container-volumes).

But recently I stumbled on this which for some reason (?) recommends using the opposite from bottom-to-top:

"To check and repair a disk, you need to run First Aid on each volume and container on the storage device in turn, then run it on the storage device itself."

https://support.apple.com/guide/disk-utility/repair-a-storage-device-dskutl1040/mac

...and in Big Sur 11.6.2 Recovery mode I now get the following alerts:

"warning: container has been mounted by APFS version 1933.61.1, which is newer than 1677.141.2"

"warning: disabling overallocation repairs by default; use -o to override"

"warning: orphan omap mappings found for oid range 682964 --> 682976

"warning: Unable to read apfs keylocker ranges: No such file or directory"

...but in (Monterey?) Internet Recovery mode there are no such alerts. Go figure?

https://developer.apple.com/forums/thread/664893

https://apple.stackexchange.com/questions/372797/macos-catalina-cant-mount-external-hdd-verification-reading-of-the-omap-obj

You really have to run FIrst Aid on the top level disk and the container and each volume separately.

As you likely know to do First Aid on the startup disk you have to boot to Recovery.

In 30+ years of using a Mac, I've never checked the well-being of any of the various and sundry Macs I've owned. If it starts acting funny, check the disk.

You will likely affect your mental well-being running First Aid on an APFS volume. There will be many scary entries in the log that appear to mean absolutely nothing. If the Mac is running well, and you run First Aid which "fixes" various things that are "incorrect," was there really anything wrong and are you causing more harm that good?

or do I have to run First Aid for each and every volume and container listed? Thanks for any help you can offer with this question :-)

As noted, you have to run each separately. Each level is checked for different things. Starting at the top of the hierarchy does not check the lower levels.

I avoid getting all the scary alerts that might otherwise show up if one lets a year or more go by without running the procedure. This approach has served me well for the several decades I've owned Macs.

I have run my Macs for over 30 years without running First Aid on them unless I get some weird behavior.

I have never received a "scary" alert on any of them. My 2012 Mini has been running continuously since I purchased it. No First Aid, no scary alerts.

You are wasting your time. You don’t need to run Disk First Aid at all, let alone weekly. It does much, much less than most people think.